In this paper,we propose a map that connects nucleons bound in nuclei and Ising spins in the Ising model.This proposal is based on the fact that the description of states of nucleons and Ising spins could share the sa...In this paper,we propose a map that connects nucleons bound in nuclei and Ising spins in the Ising model.This proposal is based on the fact that the description of states of nucleons and Ising spins could share the same type of observables.We present a nuclear model corresponding to an explicit modified Ising model and qualitatively confirm the correctness of this map with a simulation on a two-dimensional square lattice.This map can help us understand the profound connections between different physical systems.展开更多
This note introduces a method for sampling Ising models with mixed boundary conditions.As an application of annealed importance sampling and the Swendsen-Wang algorithm,the method adopts a sequence of intermediate dis...This note introduces a method for sampling Ising models with mixed boundary conditions.As an application of annealed importance sampling and the Swendsen-Wang algorithm,the method adopts a sequence of intermediate distributions that keeps the temperature fixed but turns on the boundary condition gradually.The numerical results show that the variance of the sample weights is relatively small.展开更多
This note introduces the double flip move to accelerate the Swendsen-Wang algorithm for Ising models with mixed boundary conditions below the critical temperature.The double flip move consists of a geometric flip of t...This note introduces the double flip move to accelerate the Swendsen-Wang algorithm for Ising models with mixed boundary conditions below the critical temperature.The double flip move consists of a geometric flip of the spin lattice followed by a spin value flip.Both symmetric and approximately symmetric models are considered.We prove the detailed balance of the double flip move and demonstrate its empirical efficiency in mixing.展开更多
Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to ver...Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.展开更多
Quantum computing is a field with increasing relevance as quantum hardware improves and more applications of quantum computing are discovered. In this paper, we demonstrate the feasibility of modeling Ising Model Hami...Quantum computing is a field with increasing relevance as quantum hardware improves and more applications of quantum computing are discovered. In this paper, we demonstrate the feasibility of modeling Ising Model Hamiltonians on the IBM quantum computer. We developed quantum circuits to simulate these systems more efficiently for both closed and open boundary Ising models, with and without perturbations. We tested these various geometries of systems in both 1-D and 2-D space to mimic two real systems: magnetic materials and biological neural networks (BNNs). Our quantum model is more efficient than classical computers, which can struggle to simulate large, complex systems of particles.展开更多
Many phenomena show that in a favorable circumstance an agent still has an updating possibility, and in an unfavor- able circumstance an agent also has a possibility of holding its own state and reselecting its neighb...Many phenomena show that in a favorable circumstance an agent still has an updating possibility, and in an unfavor- able circumstance an agent also has a possibility of holding its own state and reselecting its neighbors. To describe this kind of phenomena an Ising model on evolution networks was presented and used for consensus formation and separation of opinion groups in human population. In this model the state-holding probability p and selection-rewiring probability q were introduced. The influence of this mixed dynamics of spin flips and network rewiring on the ordering behavior of the model was investigated, p hinders ordering of opinion networks and q accelerates the dynamical process of networks. Influence of q on the ordering and separating stems from its effect on average path length of networks.展开更多
An overview of the mathematical structure of the three-dimensional(3D) Ising model is given from the points of view of topology,algebra,and geometry.By analyzing the relationships among transfer matrices of the 3D I...An overview of the mathematical structure of the three-dimensional(3D) Ising model is given from the points of view of topology,algebra,and geometry.By analyzing the relationships among transfer matrices of the 3D Ising model,Reidemeister moves in the knot theory,Yang-Baxter and tetrahedron equations,the following facts are illustrated for the 3D Ising model.1) The complex quaternion basis constructed for the 3D Ising model naturally represents the rotation in a(3+1)-dimensional space-time as a relativistic quantum statistical mechanics model,which is consistent with the 4-fold integrand of the partition function obtained by taking the time average.2) A unitary transformation with a matrix that is a spin representation in 2 n·l·o-space corresponds to a rotation in 2n·l·o-space,which serves to smooth all the crossings in the transfer matrices and contributes the non-trivial topological part of the partition function of the 3D Ising model.3) A tetrahedron relationship would ensure the commutativity of the transfer matrices and the integrability of the 3D Ising model,and its existence is guaranteed by the Jordan algebra and the Jordan-von Neumann-Wigner procedures.4) The unitary transformation for smoothing the crossings in the transfer matrices changes the wave functions by complex phases φx,φy,and φz.The relationship with quantum field and gauge theories and the physical significance of the weight factors are discussed in detail.The conjectured exact solution is compared with numerical results,and the singularities at/near infinite temperature are inspected.The analyticity in β=1/(kBT) of both the hard-core and the Ising models has been proved only for β〉0,not for β=0.Thus the high-temperature series cannot serve as a standard for judging a putative exact solution of the 3D Ising model.展开更多
The review paper by Zhang Zhi-Dong (Zhang Z D 2013 Chin. Phys. B 22 030513, arXiv:1305.2956) contains many errors and is based on several earlier works that are equally wrong.
We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined ...We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L=8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at Тc=3.6403(2). A convincing finite-size scaling analysis of the model yields ν=0.9995(21), β/ν=0.12400(17), γ/v=1.75223(22), γ^1/ν=1.7555(22), α/ν=0.00077(420) (scaling) and α/ν=0.0010(42) (hyperscaling). The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.展开更多
Recently, Shiet al. [2008 Phys. Left. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an e...Recently, Shiet al. [2008 Phys. Left. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tome and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tome and de Oliveira; hence the dynamic phase diagrams calculated by Shiet al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (w) and static external field amplitude (h0) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of w and h0.展开更多
We present a multifractal detrended fluctuation analysis (MFDFA) of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the M...We present a multifractal detrended fluctuation analysis (MFDFA) of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the MFDFA shows that there exists obvious multifractal scaling behavior in produced time series. We compare the MFDFA results for original time series with those for shuffled series, and find that its multifractal nature is due to two factors: broadness of probability density function of the series and different correlations in small- and large-scale fluctuations. This may provide new insight to the problem of the origin of multifractality in financial time series.展开更多
We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies JA-...We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies JA-A and JA--B in this lattice. Our study is focused on how the ratio of JA-B to JA--A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter, the specific heat, susceptibility, etc each as a function of temperature for a given ratio of JA-B to JA-A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio JA-B / JA--A. This work is helpful for studying the phase transition problem of crystals composed of compounds.展开更多
The dynamical properties of one-dimensional random transverse Ising model (RTIM) with a double-Gaussian disorder is investigated by the recursion method. Based on the first twelve recurrences derived analytically, t...The dynamical properties of one-dimensional random transverse Ising model (RTIM) with a double-Gaussian disorder is investigated by the recursion method. Based on the first twelve recurrences derived analytically, the spin autocorrelation function (SAF) and associated spectral density at high temperature were obtained numerically. Our results indicate that when the standard deviation σg (or OrB) of the exchange couplings Ji (or the random transverse fields Bi) is small, no long-time tail appears in the SAE The spin system undergoes a crossover from a central-peak behavior to a collectivemode behavior, which is the dynamical characteristics of RTIM with the bimodal disorder. However, when σJ (or σB) is large enough, the system exhibits similar dynamics behaviors to those of the RTIM with the Gaussian disorder, i.e., the system exhibits an enhanced central-peak behavior for large σJ or a disordered behavior for large σB. In this instance, SAFs exhibit a similar long-time tail, i.e., C(t) ~ t ^-2 for large t. Similar properties are obtained when Ji (or Bi) satisfy the double-exponential distribution or the double-uniform distribution. Besides, when both the standard deviations and the mean values of the exchange couplings are small, the effects of the Gaussian random bonds may drive the system undergo two crossovers from a triplet state to a doublet state, and then to a collective-mode state.展开更多
As a problem in data science the inverse Ising(or Potts)problem is to infer the parameters of a Gibbs-Boltzmann distributions of an Ising(or Potts)model from samples drawn from that distribution.The algorithmic and co...As a problem in data science the inverse Ising(or Potts)problem is to infer the parameters of a Gibbs-Boltzmann distributions of an Ising(or Potts)model from samples drawn from that distribution.The algorithmic and computational interest stems from the fact that this inference task cannot be carried out efficiently by the maximum likelihood criterion,since the normalizing constant of the distribution(the partition function)cannot be calculated exactly and efficiently.The practical interest on the other hand flows from several outstanding applications,of which the most well known has been predicting spatial contacts in protein structures from tables of homologous protein sequences.Most applications to date have been to data that has been produced by a dynamical process which,as far as it is known,cannot be expected to satisfy detailed balance.There is therefore no a priori reason to expect the distribution to be of the Gibbs-Boltzmann type,and no a priori reason to expect that inverse Ising(or Potts)techniques should yield useful information.In this review we discuss two types of problems where progress nevertheless can be made.We find that depending on model parameters there are phases where,in fact,the distribution is close to Gibbs-Boltzmann distribution,a non-equilibrium nature of the under-lying dynamics notwithstanding.We also discuss the relation between inferred Ising model parameters and parameters of the underlying dynamics.展开更多
The dynamic phase transition properties for ferroelectric nanotube under a spin-1/2 transverse Ising model are studied under the effective field theory(EFT)with correlations.The temperature effects on the pseudo-spin ...The dynamic phase transition properties for ferroelectric nanotube under a spin-1/2 transverse Ising model are studied under the effective field theory(EFT)with correlations.The temperature effects on the pseudo-spin systems are unveiled in three-dimensional(3-D)and two-dimensional(2-D)phase diagrams.Moreover,the dynamic behaviors of exchange interactions on the 3-D and 2-D phase transitions under high temperature are exhibited.The results present that it is hard to obtain pure ferroelectric phase under high temperature;that is,the vibration of orderly pseudo-spins cannot be eliminated completely.展开更多
An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this ...An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this model is developed to calculate the electrical and magnetic properties of Ca3CoMnO6, a typical quasi-one-dimensional diatomic spin chain system. The calculated ferroelectric polarization and dielectric susceptibility show a good agreement with recently reported data on Ca3Co2-xMnxO6 (x ≈ 0.96) (Phys. Rev. Lett. 100 047601 (2008)), although the predicted magnetic susceptibility does not coincide well with experiment. We also address the rationality and deficiency of this model by including a first-order correction which improves the consistency between the model and experiment.展开更多
We present a study of the dynamic behavior of a two-sublattice spin-5/2 Ising model with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on alternating l...We present a study of the dynamic behavior of a two-sublattice spin-5/2 Ising model with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on alternating layers of a hexagonal lattice by using the Glauber-type stochastic dynamics.The lattice is formed by alternate layers of spins σ=5/2 and S=5/2.We employ the Glauber transition rates to construct the mean-field dynamic equations.First,we investigate the time variations of the average sublattice magnetizations to find the phases in the system and then the thermal behavior of the dynamic sublattice magnetizations to characterize the nature(first-or second-order) of the phase transitions and to obtain the dynamic phase transition(DPT) points.We also study the thermal behavior of the dynamic total magnetization to find the dynamic compensation temperature and to determine the type of the dynamic compensation behavior.We present the dynamic phase diagrams,including the dynamic compensation temperatures,in nine different planes.The phase diagrams contain seven different fundamental phases,thirteen different mixed phases,in which the binary and ternary combination of fundamental phases and the compensation temperature or the L-type behavior strongly depend on the interaction parameters.展开更多
We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free ferm...We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.展开更多
It was first proposed that an extended chain Ising (ECI) model contains the Ising chain model, single spin doublewell potentials and a pure phonon heat bath of a specific energy exchange with the spins. The extensio...It was first proposed that an extended chain Ising (ECI) model contains the Ising chain model, single spin doublewell potentials and a pure phonon heat bath of a specific energy exchange with the spins. The extension method is easy to apply to high dimensional cases. Then the single spin-flip probability (rate) of the ECI model is deduced based on the Boltzmann principle and general statistical principles of independent events and the model is simplified to an extended chain Glauber-Ising (ECGI) model. Moreover, the relaxation dynamics of the ECGI model were simulated by the Monte Carlo method and a comparison with the predictions of the special chain Clauber-Ising (SCGI) model was presented. It was found that the results of the two models are consistent with each other when the Ising chain length is large enough and temperature is relative low, which is the most valuable case of the model applications. These show that the ECI model will provide a firm physical base for the widely used single spin-flip rate proposed by Glauber and a possible route to obtain the single spin-flip rate of other form and even the multi-spin-flip rate.展开更多
Further to the investigation of the critical properties of the Potts model with <em>q</em> = 3 and 8 states in one dimension (1D) on directed small-world networks reported by Aquino and Lima, which present...Further to the investigation of the critical properties of the Potts model with <em>q</em> = 3 and 8 states in one dimension (1D) on directed small-world networks reported by Aquino and Lima, which presents, in fact, a second-order phase transition with a new set of critical exponents, in addition to what was reported in Sumour and Lima in studying Ising model on non-local directed small-world for several values of probability 0 < <em>P</em> < 1. In this paper the behavior of two models discussed previously, will be re-examined to study differences between their behavior on directed small-world networks for networks of different values of probability <em>P</em> = 0.1, 0.2, 0.3, 0.4 and 0.5 with different lattice sizes <em>L</em> = 10, 20, 30, 40, and 50 to compare between the important physical variables between Ising and Potts models on the directed small-world networks. We found in our paper that is a phase transitions in both Ising and Potts models depending essentially on the probability <em>P</em>.展开更多
基金supported in part by the National Natural Science Foundation of China(12105247)the China Postdoctoral Science Foundation(2021M702957)supported in part by the National Natural Science Foundation of China(12002209)。
文摘In this paper,we propose a map that connects nucleons bound in nuclei and Ising spins in the Ising model.This proposal is based on the fact that the description of states of nucleons and Ising spins could share the same type of observables.We present a nuclear model corresponding to an explicit modified Ising model and qualitatively confirm the correctness of this map with a simulation on a two-dimensional square lattice.This map can help us understand the profound connections between different physical systems.
文摘This note introduces a method for sampling Ising models with mixed boundary conditions.As an application of annealed importance sampling and the Swendsen-Wang algorithm,the method adopts a sequence of intermediate distributions that keeps the temperature fixed but turns on the boundary condition gradually.The numerical results show that the variance of the sample weights is relatively small.
文摘This note introduces the double flip move to accelerate the Swendsen-Wang algorithm for Ising models with mixed boundary conditions below the critical temperature.The double flip move consists of a geometric flip of the spin lattice followed by a spin value flip.Both symmetric and approximately symmetric models are considered.We prove the detailed balance of the double flip move and demonstrate its empirical efficiency in mixing.
基金Project supported by the Open Project of the Key Laboratory of Xinjiang Uygur Autonomous Region,China(Grant No.2021D04015)the Yili Kazakh Autonomous Prefecture Science and Technology Program Project,China(Grant No.YZ2022B021).
文摘Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.
文摘Quantum computing is a field with increasing relevance as quantum hardware improves and more applications of quantum computing are discovered. In this paper, we demonstrate the feasibility of modeling Ising Model Hamiltonians on the IBM quantum computer. We developed quantum circuits to simulate these systems more efficiently for both closed and open boundary Ising models, with and without perturbations. We tested these various geometries of systems in both 1-D and 2-D space to mimic two real systems: magnetic materials and biological neural networks (BNNs). Our quantum model is more efficient than classical computers, which can struggle to simulate large, complex systems of particles.
基金supported by the National Natural Science Foundation of China(Grant No.11304123)the Scientific Research Foundation of Jianghan University(Grant No.2010014)
文摘Many phenomena show that in a favorable circumstance an agent still has an updating possibility, and in an unfavor- able circumstance an agent also has a possibility of holding its own state and reselecting its neighbors. To describe this kind of phenomena an Ising model on evolution networks was presented and used for consensus formation and separation of opinion groups in human population. In this model the state-holding probability p and selection-rewiring probability q were introduced. The influence of this mixed dynamics of spin flips and network rewiring on the ordering behavior of the model was investigated, p hinders ordering of opinion networks and q accelerates the dynamical process of networks. Influence of q on the ordering and separating stems from its effect on average path length of networks.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50831006)
文摘An overview of the mathematical structure of the three-dimensional(3D) Ising model is given from the points of view of topology,algebra,and geometry.By analyzing the relationships among transfer matrices of the 3D Ising model,Reidemeister moves in the knot theory,Yang-Baxter and tetrahedron equations,the following facts are illustrated for the 3D Ising model.1) The complex quaternion basis constructed for the 3D Ising model naturally represents the rotation in a(3+1)-dimensional space-time as a relativistic quantum statistical mechanics model,which is consistent with the 4-fold integrand of the partition function obtained by taking the time average.2) A unitary transformation with a matrix that is a spin representation in 2 n·l·o-space corresponds to a rotation in 2n·l·o-space,which serves to smooth all the crossings in the transfer matrices and contributes the non-trivial topological part of the partition function of the 3D Ising model.3) A tetrahedron relationship would ensure the commutativity of the transfer matrices and the integrability of the 3D Ising model,and its existence is guaranteed by the Jordan algebra and the Jordan-von Neumann-Wigner procedures.4) The unitary transformation for smoothing the crossings in the transfer matrices changes the wave functions by complex phases φx,φy,and φz.The relationship with quantum field and gauge theories and the physical significance of the weight factors are discussed in detail.The conjectured exact solution is compared with numerical results,and the singularities at/near infinite temperature are inspected.The analyticity in β=1/(kBT) of both the hard-core and the Ising models has been proved only for β〉0,not for β=0.Thus the high-temperature series cannot serve as a standard for judging a putative exact solution of the 3D Ising model.
文摘The review paper by Zhang Zhi-Dong (Zhang Z D 2013 Chin. Phys. B 22 030513, arXiv:1305.2956) contains many errors and is based on several earlier works that are equally wrong.
基金Project supported partially by Guangdong Natural Science Foundation (GDNSF) of China (Grant No 07300793)One of authors(Loan Mushtaq) was partially supported by the Guangdong Ministry of Education,China
文摘We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L=8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at Тc=3.6403(2). A convincing finite-size scaling analysis of the model yields ν=0.9995(21), β/ν=0.12400(17), γ/v=1.75223(22), γ^1/ν=1.7555(22), α/ν=0.00077(420) (scaling) and α/ν=0.0010(42) (hyperscaling). The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.
基金Project supported by the Scientific and Technological Research Council of Turkey (TBTAK) (Grant No. 107T533)the Erciyes University Research Funds (Grant Nos. FBA-06-01 and FBD-08-593)
文摘Recently, Shiet al. [2008 Phys. Left. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tome and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tome and de Oliveira; hence the dynamic phase diagrams calculated by Shiet al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (w) and static external field amplitude (h0) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of w and h0.
基金Supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars of State Education Ministry
文摘We present a multifractal detrended fluctuation analysis (MFDFA) of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the MFDFA shows that there exists obvious multifractal scaling behavior in produced time series. We compare the MFDFA results for original time series with those for shuffled series, and find that its multifractal nature is due to two factors: broadness of probability density function of the series and different correlations in small- and large-scale fluctuations. This may provide new insight to the problem of the origin of multifractality in financial time series.
基金supported by the National Natural Science Foundation of China(Grant No 10571091)the National Science and Technology Supporting Program of China(Grant No 2006BAD11A07)
文摘We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies JA-A and JA--B in this lattice. Our study is focused on how the ratio of JA-B to JA--A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter, the specific heat, susceptibility, etc each as a function of temperature for a given ratio of JA-B to JA-A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio JA-B / JA--A. This work is helpful for studying the phase transition problem of crystals composed of compounds.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11302118 and 11275112)the Natural Science Foundation of Shandong Province of China(Grant Nos.ZR2013AQ015 and ZR2011AM018)the Postdoctoral Science Foundation of Qufu Normal University(Grant No.BSQD2012053)
文摘The dynamical properties of one-dimensional random transverse Ising model (RTIM) with a double-Gaussian disorder is investigated by the recursion method. Based on the first twelve recurrences derived analytically, the spin autocorrelation function (SAF) and associated spectral density at high temperature were obtained numerically. Our results indicate that when the standard deviation σg (or OrB) of the exchange couplings Ji (or the random transverse fields Bi) is small, no long-time tail appears in the SAE The spin system undergoes a crossover from a central-peak behavior to a collectivemode behavior, which is the dynamical characteristics of RTIM with the bimodal disorder. However, when σJ (or σB) is large enough, the system exhibits similar dynamics behaviors to those of the RTIM with the Gaussian disorder, i.e., the system exhibits an enhanced central-peak behavior for large σJ or a disordered behavior for large σB. In this instance, SAFs exhibit a similar long-time tail, i.e., C(t) ~ t ^-2 for large t. Similar properties are obtained when Ji (or Bi) satisfy the double-exponential distribution or the double-uniform distribution. Besides, when both the standard deviations and the mean values of the exchange couplings are small, the effects of the Gaussian random bonds may drive the system undergo two crossovers from a triplet state to a doublet state, and then to a collective-mode state.
基金the National Natural Science Foundation of China(Grant No.11705097)the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20170895)+1 种基金the Jiangsu Government Scholarship for Overseas Studies of 2018 and Scientific Research Foundation of Nanjing University of Posts and Telecommunications,China(Grant No.NY217013)the Foundation for Polish Science through TEAM-NET Project(Grant No.POIR.04.04.00-00-17C1/18-00).
文摘As a problem in data science the inverse Ising(or Potts)problem is to infer the parameters of a Gibbs-Boltzmann distributions of an Ising(or Potts)model from samples drawn from that distribution.The algorithmic and computational interest stems from the fact that this inference task cannot be carried out efficiently by the maximum likelihood criterion,since the normalizing constant of the distribution(the partition function)cannot be calculated exactly and efficiently.The practical interest on the other hand flows from several outstanding applications,of which the most well known has been predicting spatial contacts in protein structures from tables of homologous protein sequences.Most applications to date have been to data that has been produced by a dynamical process which,as far as it is known,cannot be expected to satisfy detailed balance.There is therefore no a priori reason to expect the distribution to be of the Gibbs-Boltzmann type,and no a priori reason to expect that inverse Ising(or Potts)techniques should yield useful information.In this review we discuss two types of problems where progress nevertheless can be made.We find that depending on model parameters there are phases where,in fact,the distribution is close to Gibbs-Boltzmann distribution,a non-equilibrium nature of the under-lying dynamics notwithstanding.We also discuss the relation between inferred Ising model parameters and parameters of the underlying dynamics.
基金Project supported by the National Key R&D Program of China(Grant No.2017YFE0120500)the National Natural Science Foundation of China(Grant No.51972129)+3 种基金the South Xinjiang Innovation and Development Program of Key Industries of Xinjiang Production and Construction Corps(Grant No.2020DB002)the Fundamental Research Funds for the Central Universities,China(Grant Nos.HUST 2018KFYYXJJ051 and 2019KFYXMBZ076)Shenzhen Fundamental Research Fund(Grant No.JCYJ20190813172609404)the Hubei“Chu-Tian Young Scholar”Program。
文摘The dynamic phase transition properties for ferroelectric nanotube under a spin-1/2 transverse Ising model are studied under the effective field theory(EFT)with correlations.The temperature effects on the pseudo-spin systems are unveiled in three-dimensional(3-D)and two-dimensional(2-D)phase diagrams.Moreover,the dynamic behaviors of exchange interactions on the 3-D and 2-D phase transitions under high temperature are exhibited.The results present that it is hard to obtain pure ferroelectric phase under high temperature;that is,the vibration of orderly pseudo-spins cannot be eliminated completely.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 50832002,10674061 and 10874075)the National Key Projects for Basic Research of China (Grant Nos 2006CB921802 and 2009CB623303)
文摘An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this model is developed to calculate the electrical and magnetic properties of Ca3CoMnO6, a typical quasi-one-dimensional diatomic spin chain system. The calculated ferroelectric polarization and dielectric susceptibility show a good agreement with recently reported data on Ca3Co2-xMnxO6 (x ≈ 0.96) (Phys. Rev. Lett. 100 047601 (2008)), although the predicted magnetic susceptibility does not coincide well with experiment. We also address the rationality and deficiency of this model by including a first-order correction which improves the consistency between the model and experiment.
文摘We present a study of the dynamic behavior of a two-sublattice spin-5/2 Ising model with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on alternating layers of a hexagonal lattice by using the Glauber-type stochastic dynamics.The lattice is formed by alternate layers of spins σ=5/2 and S=5/2.We employ the Glauber transition rates to construct the mean-field dynamic equations.First,we investigate the time variations of the average sublattice magnetizations to find the phases in the system and then the thermal behavior of the dynamic sublattice magnetizations to characterize the nature(first-or second-order) of the phase transitions and to obtain the dynamic phase transition(DPT) points.We also study the thermal behavior of the dynamic total magnetization to find the dynamic compensation temperature and to determine the type of the dynamic compensation behavior.We present the dynamic phase diagrams,including the dynamic compensation temperatures,in nine different planes.The phase diagrams contain seven different fundamental phases,thirteen different mixed phases,in which the binary and ternary combination of fundamental phases and the compensation temperature or the L-type behavior strongly depend on the interaction parameters.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB30000000)the National Natural Science Foundation of China(Grant Nos.11774398 and T2121001)。
文摘We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.
基金supported by the National Natural Science Foundation of China (Grant Nos.10774064 and 30860076)Xinjiang High-Tech Development Foundation (Grant No.200916126)the Key Natural Science Foundation of Xinjiang Science-Technology Department (Grant Nos.200821104 and 200821184)
文摘It was first proposed that an extended chain Ising (ECI) model contains the Ising chain model, single spin doublewell potentials and a pure phonon heat bath of a specific energy exchange with the spins. The extension method is easy to apply to high dimensional cases. Then the single spin-flip probability (rate) of the ECI model is deduced based on the Boltzmann principle and general statistical principles of independent events and the model is simplified to an extended chain Glauber-Ising (ECGI) model. Moreover, the relaxation dynamics of the ECGI model were simulated by the Monte Carlo method and a comparison with the predictions of the special chain Clauber-Ising (SCGI) model was presented. It was found that the results of the two models are consistent with each other when the Ising chain length is large enough and temperature is relative low, which is the most valuable case of the model applications. These show that the ECI model will provide a firm physical base for the widely used single spin-flip rate proposed by Glauber and a possible route to obtain the single spin-flip rate of other form and even the multi-spin-flip rate.
文摘Further to the investigation of the critical properties of the Potts model with <em>q</em> = 3 and 8 states in one dimension (1D) on directed small-world networks reported by Aquino and Lima, which presents, in fact, a second-order phase transition with a new set of critical exponents, in addition to what was reported in Sumour and Lima in studying Ising model on non-local directed small-world for several values of probability 0 < <em>P</em> < 1. In this paper the behavior of two models discussed previously, will be re-examined to study differences between their behavior on directed small-world networks for networks of different values of probability <em>P</em> = 0.1, 0.2, 0.3, 0.4 and 0.5 with different lattice sizes <em>L</em> = 10, 20, 30, 40, and 50 to compare between the important physical variables between Ising and Potts models on the directed small-world networks. We found in our paper that is a phase transitions in both Ising and Potts models depending essentially on the probability <em>P</em>.