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 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 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
The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or schedu...The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.展开更多
As a very simple model,the Ising model plays an important role in statistical physics.In the paper,with the help of quantum Liouvillian statistical theory,we study the one-dimensional nonHermitian Ising model at finit...As a very simple model,the Ising model plays an important role in statistical physics.In the paper,with the help of quantum Liouvillian statistical theory,we study the one-dimensional nonHermitian Ising model at finite temperature and give its analytical solutions.We find that the nonHermitian Ising model shows quite different properties from those of its Hermitian counterpart.For example,the‘pseudo-phase transition’is explored between the‘topological’phase and the‘nontopological’phase,at which the Liouvillian energy gap is closed rather than the usual energy gap.In particular,we point out that the one-dimensional non-Hermitian Ising model at finite temperature can be equivalent to an effective anisotropic XY model in the transverse field.This work will help people understand quantum statistical properties of non-Hermitian systems at finite temperatures.展开更多
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
In this work,the computational complexity of a spin-glass three-dimensional(3D)Ising model(for the lattice sizeN=lmn,wherel,m,n are thenumbersof lattice points along three crystallographic directions)is studied.We pro...In this work,the computational complexity of a spin-glass three-dimensional(3D)Ising model(for the lattice sizeN=lmn,wherel,m,n are thenumbersof lattice points along three crystallographic directions)is studied.We prove that an absolute minimum core(AMC)model consisting of a spin-glass 2D Ising model interacting with its nearest neighboring plane,has its computational complexity O(2mn).Any algorithms to make the model smaller(or simpler)than the AMC model will cut the basic element of the spin-glass 3D Ising model and lost many important information of the original model.Therefore,the computational complexity of the spin-glass 3D Ising model cannot be reduced to be less than O(2mn)by any algorithms,which is in subexponential time,superpolynomial.展开更多
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 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 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>.
基金supported by the National Key R&D Program of China(Grant No.2019YFA0308700)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301500)。
文摘The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.
文摘As a very simple model,the Ising model plays an important role in statistical physics.In the paper,with the help of quantum Liouvillian statistical theory,we study the one-dimensional nonHermitian Ising model at finite temperature and give its analytical solutions.We find that the nonHermitian Ising model shows quite different properties from those of its Hermitian counterpart.For example,the‘pseudo-phase transition’is explored between the‘topological’phase and the‘nontopological’phase,at which the Liouvillian energy gap is closed rather than the usual energy gap.In particular,we point out that the one-dimensional non-Hermitian Ising model at finite temperature can be equivalent to an effective anisotropic XY model in the transverse field.This work will help people understand quantum statistical properties of non-Hermitian systems at finite temperatures.
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This work has been supported by the National Natural Science Foundation of China under grant numbers 51590883 and 51331006by the State Key Project of Research and Development of China(No.2017YFA0206302).
文摘In this work,the computational complexity of a spin-glass three-dimensional(3D)Ising model(for the lattice sizeN=lmn,wherel,m,n are thenumbersof lattice points along three crystallographic directions)is studied.We prove that an absolute minimum core(AMC)model consisting of a spin-glass 2D Ising model interacting with its nearest neighboring plane,has its computational complexity O(2mn).Any algorithms to make the model smaller(or simpler)than the AMC model will cut the basic element of the spin-glass 3D Ising model and lost many important information of the original model.Therefore,the computational complexity of the spin-glass 3D Ising model cannot be reduced to be less than O(2mn)by any algorithms,which is in subexponential time,superpolynomial.