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.     

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.     

Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule

Previous studies suggest that there are three different jam phases in the cellular automata automaton model with a slow-to-start rule under open boundaries.In the present paper,the dynamics of each free-flow-jam phase transition is studied.By analysing the microscopic behaviour of the traffic flow,we obtain analytical results on the phase transition dynamics.Our results can describe the detailed time evolution of the system during phase transition,while they provide good approximation for the numerical simulation data.These findings can perfectly explain the microscopic mechanism and details of the boundary-triggered phase transition dynamics.     

Percolation and spreading of damage in a simplified Kauffman model

A simplified version of the Kauffman cellular automaton is introduced. As in the usual Kauffman model, there is a transition between a frozen phase and a chaotic phase where damage may spread. We associate the onset of chaos in this model with a percolation transition of certain rules occurring in the model. It seems to be in a different universality class from the usual Kauffman cellular automaton.     

Kaleidoscope of life: A 24-neighbourhood outer-totalistic cellular automaton

One of the challenges of cellular automaton research is finding models with a low complexity and at the same time a rich dynamics. A measure of low complexity is the number of states in the model and the number of transition rules to switch between those states. In this paper, we propose a 2-dimensional 2-state cellular automaton that-though governed by a single simple transition rule-has a sufficiently rich dynamics to be computationally universal. According to the transition rule, a cell’s state is determined by the sum of the states of the cells at orthogonal or diagonal distances one or two from the cell (distance-2 Moore neighbourhood), but not by the previous state of the cell itself. Notwithstanding its simplicity, this model is able to generate a great variety of patterns, including several types of stable configurations, oscillators and patterns that move over cellular space (gliders). We prove the computational universality of the model by constructing a universal set of logic gates (NOT and AND) from these patterns. A key element in this proof is the shifting of phases and positions of signals such that they meet the input requirements of the logic gates. Similarities of the model with classical spin systems are also discussed.     

两种扩展Harper模型的波包动力学

本文通过二次矩M₂(t)和概率分布W_n(t)数值地研究了两种扩展Harper模型的波包动力学,得到了这两种模型中各个相、各条临界线以及三相点的波包扩散情况.对于第一种扩展Harper模型,发现两个金属相中波包是弹道扩散的,在绝缘体相中波包不扩散,而在三相点以及各条临界线上波包是反常扩散的.同时,发现金属相—金属相转变的临界线上的波包动力学行为与金属相—绝缘体相转变的临界线上的相同,但三相点的动力学行为与各临 关键词： 金属绝缘体转变 扩展Harper模型 波包动力学     

Mixing Times for the Mean-Field Blume-Capel Model via Aggregate Path Coupling

We investigate the relationship between the mixing times of the Glauber dynamics of a statistical mechanical system with its thermodynamic equilibrium structure. For this we consider the mean-field Blume-Capel model, one of the simplest statistical mechanical models that exhibits the following intricate phase transition structure: within a two-dimensional parameter space there exists a curve at which the model undergoes a second-order, continuous phase transition, a curve where the model undergoes a first-order, discontinuous phase transition, and a tricritical point which separates the two curves. We determine the interface between the regions of slow and rapid mixing. In order to completely determine the region of rapid mixing, we employ a novel extension of the path coupling method, successfully proving rapid mixing even in the absence of contraction between neighboring states.     

Dynamics of a quantum phase transition

We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatment of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses Landau-Zener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.     

van der Waals-like transition in fluidized granular matter

A phase separation of fluidized granular matter is presented. Molecular dynamics simulations of a system of grains in two spatial dimensions, with a vibrating wall and without gravity, exhibit the appearance, coalescence, and disappearance of bubbles. By identifying the mechanism responsible for the phase separation, we show that the phenomenon is analogous to the spinodal decomposition of the gas-liquid transition of the van der Waals model. We have deduced a macroscopic model for the onset of phase separation which agrees quite well with molecular dynamics simulations.     

Dynamic critical behavior near the superfluid transition in 3He-4He mixtures in two loop order

We calculated in two loop order the field theoretic renormalization group functions taking into account the decomposition of the dynamical vertex functions into the static vertex functions and genuine dynamical parts. The observation of this nonperturbative structure simplifies the theoretical expressions obtained by perturbation theory considerably and makes tractable a complete two loop calculation of the critical dynamics near the superfluid transition of 3He-4He mixtures (model F'). As a result, we obtain various transport coefficients, which govern the nonasymptotic and nonuniversal temperature dependence. We also correct long-standing results for the critical dynamics of the superfluid transition in pure 4He (model F) and for the dynamics of structural or magnetic phase transitions (model C).     

Phase transition,formation and fragmentation of fullerenes

We present a statistical mechanics model treating the formation and the fragmentation of fullerenes as a phase transition. Based on this model, we investigate the formation and fragmentation of C₆₀ and C₂₄₀ fullerenes from and to a gas of carbon dimers by means of molecular dynamics (MD) simulations. These simulations were conducted for 500 ns using a topologically-constrained forcefield. At the phase transition temperature, both the cage and gaseous phases were found to coexist and the system continuously oscillates between the two phases. Combining the results of the MD simulations and the statistical mechanics approach, we obtain the dependence of the phase transition temperature on pressure and compare the results of our model with arc-discharge experiments.     

A damage model based on failure threshold weakening

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long-range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size L is increased for fixed R. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model.     

Consensus and ordering in language dynamics

We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB) state. Proposed in the context of language competition and emergence, the AB state was associated with bilingualism and synonymy respectively. We show that the two models are equivalent in the mean field approximation, though the differences at the microscopic level have non-trivial consequences. To point them out, we investigate an extension of these dynamics in which confidence/trust is considered, focusing on the case of an underlying fully connected graph, and we show that the consensus-polarization phase transition taking place in the Naming Game is not observed in the AB model. We then consider the interface motion in regular lattices. Qualitatively, both models show the same behavior: a diffusive interface motion in a one-dimensional lattice, and a curvature driven dynamics with diffusing stripe-like metastable states in a two-dimensional one. However, in comparison to the Naming Game, the AB-model dynamics is shown to slow down the diffusion of such configurations.     

Non-equilibrium Dynamics of an Optomechanical Dicke Model

Motivated by the experimental realization of Dicke model in optical cavities, we model an optomechanical system consisting of two-level BEC atoms with transverse pumping. We investigate the transition from normal and inverted state to the superradiant phase through a detailed study of the phase portraits of the system. The rich phase portraits generated by analytical arguments display two types of superradiant phases, regions of coexistence and some portion determining the persistent oscillations. We study the time evolution of the system from any phase and discuss the role of mirror frequency in reaching their attractors. Further, we add an external mechanical pump to the mirror which is capable of changing the mirror frequency through radiation pressure and study the impact of the pump on the phase portraits and the dynamics of the system. We find the external mirror frequency changing the phase portraits and even shifting the critical transition point, thereby predicting a system with controllable phase transition.     

Non-equilibrium Dynamics of an Optomechanical Dicke Model

Motivated by the experimental realization of Dicke model in optical cavities, we model an optomechanical system consisting of two-level BEC atoms with transverse pumping. We investigate the transition from normal and inverted state to the superradiant phase through a detailed study of the phase portraits of the system. The rich phase portraits generated by analytical arguments display two types of superradiant phases, regions of coexistence and some portion determining the persistent oscillations. We study the time evolution of the system from any phase and discuss the role of mirror frequency in reaching their attractors. Further, we add an external mechanical pump to the mirror which is capable of changing the mirror frequency through radiation pressure and study the impact of the pump on the phase portraits and the dynamics of the system. We find the external mirror frequency changing the phase portraits and even shifting the critical transition point, thereby predicting a system with controllable phase transition.     

相分离液体在玻璃转变过程中的动力学性质(英文)

近年来,相分离动力学一直受到大家的关注,人们从技术和理论角度进行了研究.一个二元系统从混溶温度开始进行快速冷却,这个过程驱使两个相的形成和生长.这种自发生长过程遵从幂规律R(t)∝t~n,R(t)是在t时刻的相分离域尺寸大小,增长指数n是一个重要的量,有效的反映了相分离域的增长机制.但是对于相分离液体的玻璃转变过程的研究相对较少.本文采用分子动力学(MD)模拟方法,提出了一个新的模型——相分离液体来研究玻璃转变过程.相分离在玻璃转变过程中,过冷液体分离为两个相.我们主要研究了体系的动力学不均匀性.发现两个相的动力学性质是不均匀的,两个相的玻璃转变温度是不一样的.分析得出,相分离液体在玻璃转变过程中存在着一个动力学奇异点.说明相分离可能是引起玻璃转变系统动力学奇异性的一个原因.     

Langevin Dynamics,Large Deviations and Instantons for the Quasi-Geostrophic Model and Two-Dimensional Euler Equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.     

Boundary-induced nonequilibrium phase transition into an absorbing state

We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example, we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves according to the dynamics of a contact process. As the rate for offspring production at this site is varied, the model exhibits a phase transition from a fluctuating active phase into an absorbing state. The universal properties of the transition are analyzed by numerical simulations and approximation techniques.     

Damage Spreading in a 2D Ising Model with Swendsen–Wang Dynamics

Damage spreading for Ising cluster dynamics is investigated numerically by using random numbers in a way that conforms with the notion of submitting the two evolving replicas to the same thermal noise. Two damage spreading transitions are found; damage does not spread either at low or high temperatures. We determine some critical exponents at the high-temperature transition point, which seem consistent with directed percolation.