Magnetic properties of an anti-ferromagnetic and ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model in the longitudinal magnetic field within the effective-field approximation

The magnetic properties of an anti-ferromagnetic and ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model with a crystal field in a longitudinal magnetic field on the honeycomb (z=3) and square lattice (z=4) are studied by using the effective-field theory with correlations. The ground state phase diagram of the model is obtained in the longitudinal magnetic field (h) and a single-ion potential or crystal-field interaction (Δ) plane. We also investigate the thermal variations of the sublattice and total magnetizations, and present the phase diagrams in the (Δ/|J|, ) plane. The phase diagrams have one, two or even three compensation temperatures depending on the values of the crystal-field interaction. Moreover, the susceptibility, internal energy and specific heat of the system are numerically examined, and some interesting phenomena in these quantities are found due to the applied longitudinal magnetic field.     

Nonequilibrium phase transition in the kinetic Ising model on a two-layer square lattice under the presence of an oscillating field

The nonequilibrium or dynamic phase transitions are studied, within a mean-field approach, in the kinetic Ising model on a two-layer square lattice consisting of spin- 1/2 ions in the presence of a time varying (sinusoidal) magnetic field has been studied by using Glauber-type stochastic dynamics. The dynamic equations of motion are obtained in terms of the intralayer coupling constants J₁ and J₂ for the first and second layer, respectively, and interlayer coupling constant J₃ between these two layers. The nature (first- or second-order) of the transitions is characterized by investigating the behavior of the thermal variations of the dynamic order parameters. The dynamic phase transitions are obtained and the dynamic phase diagrams are constructed in the plane of the reduced temperature versus the amplitude of the magnetic field and found fourteen fundamental types of phase diagrams. Phase diagrams exhibit one, two or three dynamic tricritical points for various values of J₂/|J₁| and J₃/|J₁|. Besides the paramagnetic (p), ferromagnetic (f) and compensated (c) phases, there were the f+c,f+sf,c+sf,af+p,m+p,f+m and c+af, where the af, sf and m are the antiferromagnetic, surface ferromagnetic and mixed phases respectively. Coexistence phase regions also exist in the system.     

Ising model with mixed boundary conditions: Universal amplitude ratios

In the vicinity of boundaries the bulk universality class of critical phenomena splits into several boundary universality classes, depending upon whether the tendency to order in the boundary is smaller or larger than in the bulk. For Ising universality class there are five different boundary universality classes: periodic, antiperiodic, free, fixed and mixed (mixture of the last two). In this paper we present the new set of the universal amplitude ratios for the mixed boundary universality class. The results are in perfect agreement with a perturbated conformal field theory scenario proposed by Cardy [J. Cardy, Nucl. Phys. B 270 (1986) 186].     

Classical two-site fidelity and quantum phase transitions in the Ising model and the extended Hubbard model

In this Letter, the classical two-site-ground-state fidelity (CTGF) is exploited to identify quantum phase transitions (QPTs) for the transverse field Ising model (TFIM) and the one-dimensional extended Hubbard model (EHM). Our results show that the CTGF exhibits an abrupt change around the regions of criticality and can be used to identify QPTs in spin and fermionic systems. The method is especially convenient when it is connected with the density-matrix renormalization group (DMRG) algorithm.     

Discretization effect in a multi-grid egress model

In the traditional egress model based on cellular automata, building spaces are divided into discrete grids, the size of which is usually as large as that of a pedestrian. In order to explore the influences of the grid size on the evacuation results, we studied the evacuation process using a multi-grid egress model. In the multi-grid model, a finer grid is used and each pedestrian occupies n×n basic grids. It is found that if the pedestrian always moves one grid at each time step, the evacuation time increases with the decrease of the grid size, and reaches a stable, grid-independent value when the grid size is small enough. Another factor which influences the evacuation results is the length of the time step. It is found that with the increasing length of the time step, the evacuation time has a tendency to increase but endures complex changes. The differences between the single-grid model and multi-grid model may be due to two main reasons. First, in the multi-grid model, the pedestrians are out of alignment so that there are patches of unusable empty spaces as they are smaller in size than a pedestrian. Second, in the multi-grid model, pedestrians tend to reach the exit at the same time, leading to more serious conflicts among pedestrians.     

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, , alternated with spins that can take the four values, . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters.     

Absorbing phase transition in contact process on fractal lattices

We investigate the critical behavior of nonequilibrium phase transition from an active phase to an absorbing state on two selected fractal lattices, i.e., on a checkerboard fractal and on a Sierpinski carpet. The checkerboard fractal is finitely ramified with many dead ends, while the Sierpinski carpet is infinitely ramified. We measure various critical exponents of the contact process with a diffusion-reaction scheme A→AA and A→0, characterized by a spreading with a rate λ and an annihilation with a rate μ, and the results are confirmed by a crossover scaling and a finite-size scaling. The exponents, compared with the ?-expansion results assuming , being the fractal dimension of the underlying fractal lattice, exhibit significant deviations from the analytical results for both the checkerboard fractal and the Sierpinski carpet. On the other hand, the exponents on a checkerboard fractal agree well with the interpolated results of the regular lattice for the fractional dimensionality, while those on a Sierpinski carpet show marked deviations.     

Condensation and metastability in the 2D Potts model

For the first order transition of the Ising model below , Isakov has proven that the free energy possesses an essential singularity in the applied field. Such a singularity in the control parameter, anticipated by condensation theory, is believed to be a generic feature of first order transitions, but too weak to be observable. We study these issues for the temperature driven transition of the q states 2D Potts model at . Adapting the droplet model to this case, we relate its parameters to the critical properties at and confront the free energy to the many informations brought by previous works. The essential singularity predicted at the transition temperature leads to observable effects in numerical data. On a finite lattice, a metastability domain of temperatures is identified, which shrinks to zero in the thermodynamical limit. Received 30 March 1999     

Antiferromagnetic model and magnetization plateaus on the zigzag ladder with two- and three-site exchanges

The Ising approximation is proposed for the Heisenberg model with two- and three-spin exchange interactions on a zigzag ladder placed in a strong magnetic field. Using the transfer matrix technique the magnetization is calculated and compared with the results obtained in the dynamical recursive approach. Magnetization plateaus are found at m=0 and with the two- and three-spin exchanges. The magnetic susceptibility in small and large zigzag ladders for various exchange parameters and temperatures is also analyzed. As temperature decreases the magnetic susceptibility versus magnetic field shows the formation of spin pseudogaps and transformation from double to four peak structure. Small clusters also exhibit characteristic features of large thermodynamic systems.     

Phase diagram of the two-dimensional ferromagnetic three-color Ashkin-Teller model

In the present work we study the critical properties of the ferromagnetic three-color Ashkin-Teller model (3AT) by means of a Migdal-Kadanoff renormalization group approach on a diamond-like hierarchical lattice. The analysis of the fixed points and flux diagram of the recursion relations is used to determine the corresponding phase diagram (including its symmetry properties) and critical exponents. Our numerical results show the presence of four universality classes, three of them are associated to the Potts model with q=2, 4 and 6 states. Finally, a connection between our findings and some known results from the literature is presented.     

Monte Carlo simulation of the reorientation transition in Heisenberg model with dipole interactions

The change of magnetic states in ultrathin films with temperature have been simulated by Monte Carlo method. A Heisenberg model with long-range dipole interactions was adopted in our calculations. The results were qualitatively in good agreement with the experimental phenomena. That is at low temperatures the magnetization is perpendicular to the plane, and at higher temperatures but below the Curie point, the magnetization is mostly within the plane. In between these two regions, the magnetization seems to be suppressed. The simulations show that the loss of magnetization is a consequence of the special magnetic states in which the local domains orientations are reverse with the neighbor ones.     

Dynamic compensation temperature in the kinetic spin-1 Ising model in an oscillating external magnetic field on alternate layers of a hexagonal lattice

The dynamic behavior of a two-sublattice spin-1 Ising model with a crystal-field interaction (D) in the presence of a time-varying magnetic field on a hexagonal lattice is studied by using the Glauber-type stochastic dynamics. The lattice is formed by alternate layers of spins σ=1 and S=1. For this spin arrangement, any spin at one lattice site has two nearest-neighbor spins on the same sublattice, and four on the other sublattice. The intersublattice interaction is antiferromagnetic. We employ the Glauber transition rates to construct the mean-field dynamical equations. Firstly, we study time variations of the average magnetizations in order to find the phases in the system, and the temperature dependence of the average magnetizations in a period, which is also called the dynamic magnetizations, to obtain the dynamic phase transition (DPT) points as well as to characterize the nature (continuous and discontinuous) of transitions. Then, the behavior of the total dynamic magnetization as a function of the temperature is investigated to find the types of the compensation behavior. Dynamic phase diagrams are calculated for both DPT points and dynamic compensation effect. Phase diagrams contain the paramagnetic (p) and antiferromagnetic (af) phases, the p+af and nm+p mixed phases, nm is the non-magnetic phase, and the compensation temperature or the L-type behavior that strongly depend on the interaction parameters. For D<2.835 and H₀>3.8275, H₀ is the magnetic field amplitude, the compensation effect does not appear in the system.     

A new method to study phase transition in 3D Heisenberg model

It is shown that partial entropy, which is the classical analog of von Neumann entropy in quantum theory, is an effective tool to study the thermodynamic phase transitions in the physical systems. This method captures the intrinsic characters of critical fluctuations and does not need the pre-assumed order parameter. As an example, the finite temperature phase transition in the quantum three-dimensional spin-1/2 Heisenberg model is studied, where the stochastic series expansion quantum Monte Carlo method with operator-loop update is used. It is found that close to the critical temperature, the derivative of partial entropy displays a maximum value and shows finite size scaling behaviors, from which the critical temperature and critical exponents are determined.     

Subconscious Effect on Pedestrian Counter Flow

We propose an extended lattice gas model with different maximum velocities to simulate pedestrian counter flow by considering the subconscious behaviour of walkers. Four types of walkers including faster right walkers, slower right walkers, faster left walkers and slower left walkers are involved in the simulation. The simulation results show that our model can capture some essential features of pedestrian counter flows, such as the lane formation, segregation effect and phase separation at higher densities. We also find that the subconscious effect can reduce the occurrence of jam cluster evidently compared with the ease of un-subeonscious effect. At large maximum velocity, the critical density corresponding to the maximum flow rate of the fundamental diagram is in good agreement with the empirical results.     

MC-simulation of the 3D,q=3 Potts model

We consider theq=3 Potts model in three dimensions by Monte Carlo simulations. The microcanonical density of states is calculated as a function of the internal energy of the system. We extrapolate the data for the simulated finite systems to the thermo-dynamic limit and find a discontinuous phase transition. This method is checked in the two-dimensional case, where exact results are known.     

Magnetic properties of the mixed ferrimagnetic ternary system with a single-ion anisotropy on the Bethe lattice

The magnetic properties of the ternary system ABC consisting of spins , S=1, and are investigated on the Bethe lattice by using the exact recursion relations. We consider both ferromagnetic and antiferromagnetic exchange interactions. The exact expressions for magnetizations and magnetic susceptibilities are found, and thermal behaviors of magnetizations and susceptibilities are studied. We construct the phase diagrams and find that the system exhibits one, two or even three compensation temperatures depending on the values of the interaction parameters in the Hamiltonian. Moreover, the system undergoes a second-order phase transition for the coordination number q?3 and a second- and first-order phase transitions for q>3; hence the system gives a tricritical point. The system also exhibits the reentrant behaviors.     

Relaxation model of the orientational phase transition in fullerite C60

The model of thermal behavior of a thermoelastic medium is developed in the context of the Landau theory of phase transitions. In the framework of this model, two different problems are considered with allowance for order parameter relaxation: the problem of relatively slow uniform heating (cooling) of the medium under external hydrostatic pressure and the problem of order parameter relaxation at thermal isolation. A finite value of the relaxation constant τ of the order parameter is demonstrated to bring about the heating (cooling) rate dependence of the physical quantities, such as specific heat. The relaxation time of the order parameter is shown to be twice larger than the temperature relaxation time, as a consequence of the Landau expansion of the free energy.     

Effective-field theory of the Ising model with three alternative layers on the honeycomb and square lattices

The Ising model with three alternative layers on the honeycomb and square lattices is studied by using the effective-field theory with correlations. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the adjacent spins of the nearest-neighbor layers are coupled either ferromagnetically or anti-ferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the thermal variations of the magnetizations and present the phase diagrams. The phase diagrams contain the paramagnetic, ferromagnetic and anti-ferromagnetic phases, and the system also exhibits a tricritical behavior.