Comparative study on phase transition behaviors of fractional molecular field theory and random-site Ising model

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.

Leveraging Quantum Computing for the Ising Model to Simulate Two Real Systems: Magnetic Materials and Biological Neural Networks (BNNs)

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.

Nucleation of Kinetic Ising Model Under Oscillating Field

We have studied the nucleation process of a two-dimensional kinetic Ising model subject to a bias oscillating external field, focusing on how the nucleation time depends on the oscillation frequency. It is found that the nucleation time shows a clear-cut minimum with the variation of oscillation frequency, wherein the average size of the critical nuclei is the smallest, indicating that an oscillating external field with an optimal frequency can be much more favorable to the nucleation process than a constant field. We have also investigated the effect of the initial phase of the external field, which helps to illustrate the occurrence of such an interesting finding.

Ground-State Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal-Field

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/ zJ-longitudinal crystal D / zJ field plane. We find that there are the first order-order phase transitions in a very small range of D /zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions,

Ising model on evolution networks and its application on opinion formation

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.

Study of Depolarization Field Influence on Ferroelectric Films Within Transverse Ising Model

An improved transverse Ising model is proposed by taking the depolarization field effect into account. Within the framework of mean-held theory we investigate the behavior of the ferroelectric thin film. Our results show that the influence of the depolarization field is to flatten the spontaneous polarization profile and make the films more homogeneous, which is consistent with Ginzburg Landau theory. This fact shows that this model can be taken as an effective model to deal with the ferroelectric film and can be further extended to refer to quantum effect. The competition between quantum effect and depolarization field induces some interesting phenomena on ferroelectric thin films.

Mathematical structure of the three-dimensional(3D) Ising model

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.

Effect of Electron Itineracy on Magnetism of S=1／2 Ferromagnetic Ising Model

The effect of electron itineracy on the magnetism of S＝1/2 ferromagnetic Ising model is investigated by introducing a hopping term. The electron Green's function method is used to deal with this Hamiltonian. Here emphasis is made on that the magnetization is caused by the difference between the filling of spin-up and spin-down electrons.This concept is in accordance with that of band structure theory. In the zero band width limit, our results are the same as obtained by spin Green's function method. However, our method achieves more detailed physical information. The spontaneous magnetization, Curie temperature, total energy, and specific heat are calculated and investigated in detail by the densities of states. Hopping term depresses the Curie temperature but remains the order-disorder transformation still to be second order transition. Above the transition point, the energy band is the same as that of tight binding system because exchange interaction has no effect anymore. While under the transition point, the energy band splits into two subbands due to exchange interaction.

Comment on 'Mathematical structure of the three-dimensional (3D) Ising model'

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.

Demage Spreading in the Ising Model with a special Metropolis Dynamics Approach

The time evolution of the Hamming distance (damage spreading) for the and Ising models on the square lattice is performed with a special metropolis dynamics algorithm. Two distinct regimes are observed according to the temperature range for both models: a low-temperature one where the distance in the long-time limit is finite and seems not to depend on the initial distance and the system size; a high-temperature one where the distance vanishes in the long-time limit. Using the finite size scaling method, the dynamical phase transition (damage spreading transition) temperature is obtained as for the Ising model.

Dynamic phase transition of ferroelectric nanotube described by a spin-1/2 transverse Ising model

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.

Critical behaviour of the ferromagnetic Ising model on a triangular lattice

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.

Kinetic Ising model in a time-dependent oscillating external magnetic field:effective-field theory

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.

Properties of Three Pseudo-Spins in Ferroelectric or Ferro-Antiferroelectric Materials Described by a Transverse Ising Model

Ferroelectric phase diagrams and the temperature dependence of polarization,dielectric properties of the three pseudo-spin in ferroelectric or ferro-antiferroelectric systemdescribed by a transverse Ising models are investigated on the basis of the effective-Geld theorywith the differential operator technique. The effects of the transverse field and the couplingstrength between the nearest-neighboring pseudo-spin on the physical properties are discussed indetail.

Longitudinal-Random-Field Mixed Ising Model with Arbitrary Spins

The longitudinal-random-fieM mixed Ising model consisting of arbitrary spin values has been studied by the use of an effective field theory with correlations （EFT）. The phase diagrams of systems with mixed spins： σ = 1/2, S = 1; σ = 1/2, S = 3/2 are plotted. Not only the discontinuity at T = 0 K, is found when both longitudinal fields are trimodal distributed, but also the trieritical behavior is observed in these phase diagrams between the bimodal and trimodal distributions of longitudinal fields, which is different from the single-spin one. The appearance of tricritical point is independent of the coordination number and spin values.

Ising Model on an Infinite Ladder Lattice

In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.

Monte Carlo study of the antiferromagnetical Ising model on a centred honeycomb lattice

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.

Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal Field

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal field is studied within themean-field theory.The phase diagrams and magnetization curves are obtained by diagonalizing the Hamiltonian H_i ofthe Ising system numerically,and the first order-order phase transitions,the first order-disorder phase transitions,andthe second-order phase transitions are discussed in details.Reentrant phenomena occur when the value of the transversefield is not zero and the reentrant diagram is given.

Effective-Field Theory for Kinetic Ising Model on Honeycomb Lattice

As an analytical method, the effective-field theory （EFT） is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the honeycomb lattice （Z = 3）. The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. In the field amplitude ho / ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn. In contrast to previous analytical results that predicted a tricritical point separating a dynamic phase boundary line of continuous and discontinuous transitions, we find that the transition is always continuous. There is inconsistency between our results and previous analytical results, because they do not introduce sufficiently strong fluctuations.

Magnetic Properties of Transverse Ising Model under a Time Oscillating Longitudinal Field

A transverse Ising spin system, in the presence of time-dependent longitudinal field, is studied by the effective-field theory （EFT）. The effective-field equations of motion of the average magnetization are given for the simple cubic lattice （Z ---- 6） and the honeycomb lattice （Z = 3）. The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. The dynamic phase transition diagrams in ho/ZJ - F/ZJ plane and in ho/ZJ - T/ZJ plane have been drawn, and there is no dynamical tricritical point on the dynamic phase transition boundary. The effect of the thermal fluctuations upon the dynamic phase boundary has been discussed.