Critical Finite Size Scaling Relation of the Order-Parameter Probability Distribution for the Three-Dimensional Ising Model on the Creutz Cellular Automaton

We study the order parameter probability distribution at the critical point for the three-dimensional spin-1/2 and spin-1 Ising models on the simple cubic lattice under periodic boundary conditions. The finite size scaling relation for the order parameter probability distribution is tested and verified numerically by microcanonical Creutz cellular automata simulations. The state critical exponent δ, which characterizes the far tail regime of the scaling order parameter probability distribution, is estimated for three-dimensional Ising models using the cellular automaton simulations at the critical temperature. The results are in good agreement with the Monte Carlo calculations.     

Critical Exponents for the Re-entrant Phase Transitions in the Three-Dimensional Blume-Emery-Grifilths Model on the Cellular Automaton

The critical behaviour of the three-dimensional Blume-Emery-Griffiths （BEG） model ＆ investigated at D/ J = O, -0.25 and -1 in the range of-1 ≤ K/J ≤ 0 for J -- 100. The simulations are carried out on a simple cubic lattice using the heating algorithm improved from the Creutz cellular automaton （CCA ） under periodic boundary conditions. The universality of the model are obtained for re-entrant and double re-entrant phase transitions which occur at certain D/J and K/J parameters, with J and K representing the nearest-neighbour bilinear and biquadratic interactions, and D being the single-ion anisotropy parameter. The values of static critical exponents β, γ and v are estimated within the framework of the finite-size scaling theory. The results are compatible with the universal Ising critical behaviour for all continuous phase transitions in these ranges.     

Simulation of Spin-3/2 Blume-Capel Model on a Cellular Automaton with Heating and Cooling Algorithm

The spin-3/2 Blume-Capel model is studied using the heating and cooling algorithms improved from the Creutz cellular automaton (CCA). The calculations are done on various sizes of the simple cubic lattice in the 0≦D/J≦5 parameter region. The phase diagram of the model and temperature variation of the thermodynamic quantities are obtained. We confirm the existence of a critical end point within the heating calculations. However, in contrast to the heating
calculations, we do not obtain the first-order line at low temperature with cooling algorithm calculations. The results are compared with those of other theories.     

First-Order Quantum Phase Transition for Dicke Model Induced by Atom-Atom Interaction

In this article, we use the spin coherent state transformation and the ground state variational method to theoretically calculate the ground function. In order to consider the influence of the atom-atom interaction on the extended Dicke model's ground state properties, the mean photon number, the scaled atomic population and the average ground energy are displayed. Using the self-consistent field theory to solve the atom-atom interaction, we discover the system undergoes a first-order quantum phase transition from the normal phase to the superradiant phase, but a famous Dicke-type second-order quantum phase transition without the atom-atom interaction. Meanwhile, the atom-atom interaction makes the phase transition point shift to the lower atom-photon collective coupling strength.     

First-Order Phase Transition in a Modified Ziff-Gulari-Barshad Model with Self-oscillating Reactant Coverages

Using kinetic Monte Carlo simulations, we study the effect of oscillatory kinetics due to surface reconstructions on Ziff-Gulari-Barshad (ZGB) model discontinuous phase transition. To investigate the transition, we do extensive finite size scaling analysis. It is found that the discontinuous transition still exists. On inclusion of desorption in the model, the order-parameter probability distribution broadens but remains bimodal. That is, the first-order phase transition becomes weaker with increase in desorption rate.     

A Simple Model fop the First-Order Phase Transition and Met astability

An extremely simplified dynamical model is proposed to consistently explain the first-order phase transition and metastability.     

A Cellular Automaton Model for Two-Lane Traffic

We present some long time limit properties of a cellular automaton that models traffic of cars on a (infinite) two-lane road. This model, called TL184, is a natural generalization of the cellular automaton classified as 184 by Wolfram (to be abbreviated by CA184) and studied before as a model for one-lane traffic. TL184 models cars' motions on each lane by particles that interact via the CA184 rules, and cars' lane changes by a possibility for particles to flip from one CA184 to another. We calculate the infinite-time limit of the particle current in TL184, starting from a translation invariant measure, and use this result to show how the possibility of lane changes may enhance the current of cars in TL184 compared to that in a corresponding model of two non-interacting one-lane roads. We provide examples which demonstrate that even though the rules that regulate lane changes are completely symmetric, the system does not evolve to an equipartition of cars among both lanes from a given initially asymmetric distribution; moreover, the asymptotic car velocities and currents may be different on different lanes. We also show that, for a particular class of initial distributions, the asymptotic car density on a lane may be a non-monotonic function of the initial car density on this lane. Finally, we derive the current-density relation for an extended continuous-time version of TL184 with asymmetric lane-changing rules.     

Critical Behavior of the Blume-Emery-Griffiths Model for a Simple Cubic Lattice on the Cellular Automaton

The spin-1 Ising model with the nearest-neighbour bilinear and biquadratic interactions and single-ion anisotropy is simulated on a cellular automaton which improved from the Creutz cellular automaton (CCA) for a simple cubic lattice. The simulations have been made for several k=K/J and d=D/J in the 0≤d<3 and −2≤k≤0 parameter regions. We confirm the existence of the re-entrant and the successive re-entrant phase transitions near the phase boundary. The phase diagrams characterizing phase transitions are presented for comparison with those obtained from other calculations. The static critical exponents are estimated within the framework of the finite-size scaling theory at d=0, 1 and 2 in the interval −2≤k≤0. The results are compatible with the universal Ising critical behavior.     

A Realistic Cellular Automaton Model for Synchronized Traffic Flow

A cellular automaton model is proposed to consider the anticipation effect in drivers＇ behavior. It is shown that the anticipation effect can be one of the origins of synchronized traffic flow. With anticipation effect, the congested traffic flow simulated by the model exhibits the features of synchronized flow. The spatiotemporal patterns induced by an on-ramp are also consistent with the three-phase traffic theory. Since the origin of synchronized flow is still controversial, our work can shed some light on the mechanism of synchronized flow.     

Effect of Quenched Nonmagnetic Impurities on the Phase Transitions in a Three-Dimensional Potts Model

Journal of Experimental and Theoretical Physics - The influence of a weak disorder in the form of quenched nonmagnetic impurities on the phase transitions (PTs) in a three-dimensional 5-state Potts...     

Exact Solution of a Cellular Automaton for Traffic

We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g., cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion process (ASEP) with simultaneous updating of all sites. It is equivalent to a special case (v _max=1) of the Nagel–Schreckenberg model for highway traffic, which has found many applications in real-time traffic simulations. The simultaneous updating induces additional strong short-range correlations compared to other updating schemes. The stationary state is written in terms of a matrix product solution. The corresponding algebra, which expresses a system-size recursion relation for the weights of the configurations, is quartic, in contrast to previous cases, in which the algebra is quadratic. We derive the phase diagram and compute various properties such as density profiles, two-point functions, and the fluctuations in the number of particles (cars) in the system. The current and the density profiles can be mapped onto the ASEP with other time-discrete updating procedures. Through use of this mapping, our results also give new results for these models.     

The Finite Temperature Effects on the Coleman Phase Transition in Double Sine-Gordon Model

By means of the finite temperature Gaussian effective potential (FTGEP) method, the (1+1) and (2+1) dimensional quantum double sine-Gordon (DsG) field theories are studied nonperturbatively for finite temperature. The explicitly FTGEP is obtained for both (1+1) and (2+1) dimensional DaG models. The temperature-dependent Coleman phase transition conditions obtained by us would reduce to the known results g_cr² when T→0. The alternative explanation of the Coleman phase transition at finite temperature is that for fixed coupling constantg² there is a critical temperature T_cr (whose value depends ong²) such that the theory becomes unstable when the temperature of the system exceeds the critical value T_cr.     

Effect of Droplet Size on the First Order Ziff-Gulari-Barshad (ZGB) Phase Transition

We introduce a new method to analyze the coexistence region of the constant rate ensemble ZGB discontinuous transition. The method clearly delineates the spinodal and coexistence points in the constant rate ZGB model. Increase in system size reduces the gap between the spinodal and coexistence points. Next we quantify the effect of metastability by introducing a droplet/nucleus of CO occupied sites in the initial system. In systems with initial nucleus of increasing size the distance between the spinodal and the coexistence point decreases, until for a large enough droplet spanning the initial system, the spinodal and the coexistence points become indistinguishable.     

Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model

Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ-T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the Bose-Einstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.     

Synchronized Flow in a Cellular Automaton Model with Time Headway Dependent Randomization

We propose another possible mechanism of synchronized flow, i,e. that a time headway dependent randomization can exhibit synchronized flow. Based on this assumption, we present a new cellular automaton （CA） model for traffic flow, in which randomization effect is enhanced with the decrease of time headway. We study fundamental diagram and spatial-temporal diagrams of the model and perform microscopic analysis of time series data, which shows the model could reproduce synchronized flow as expected. It is also shown that a spontaneous transition from synchronized flow to jam could be observed by incorporating slow-to-start effect into the model. We expect that our work could contribute to the understanding of the real origin of synchronized flow.     

Interferometry Signatures for QCD First-Order Phase Transition in High Energy Heavy Ion Collisions

Using the technique of quantum transport of the interfering pair we examine the Hanbury-Brown-Twiss （HBT） interferometry signatures for the particle-emitting sources of pions and kaons produced in heavy ion collisions at 10-30 AGeV. The evolution of the sources is described by relativistic hydrodynamics with the first-order phase transition from quark-gluon plasma （QGP） to hadronic matter. We use quantum probability amplitudes in a path-integral formalism to calculate the two-particle correlation functions, where the effects of particle decay and multiple scattering are taken into consideration. Our model-calculated results indicate that both the HBT radii of pions and kaons increase with the system initial energy density. The HBT lifetimes of the pion and kaon sources increase significantly when the initial energy density is tuned to the phase boundary between the QGP and mixed phase. This increase of HBT lifetimes will likely appear in heavy ion collisions with an incident energy between 10-30 AGeV.     

Phase Transition of a Distance-Dependent Ising Model on the Barabasi-Albert Network

We report our investigation on the behaviour of distance-dependent Ising models, which are located on the BA model network. The interaction strength between two nodes （the spins） is considered to obey an exponential decay dependence on the geometrical distance. The Monte Carlo simulation shows a phase transition from ferromagnetism to paramagnetism, and the critical temperature approaches a constant temperature as the interaction decaying exponent increases.