Dynamic percolation transition induced by phase separation: A Monte Carlo analysis

The percolation transition of geometric clusters in the three-dimensional, simple cubic, nearest neighbor Ising lattice gas model is investigated in the temperature and concentration region inside the coexistence curve. We consider quenching experiments, where the system starts from an initially completely random configuration (corresponding to equilibrium at infinite temperature), letting the system evolve at the considered temperature according to the Kawasaki spinexchange dynamics. Analyzing the distributionn _l(t) of clusters of sizel at timet, we find that after a time of the order of about 100 Monte Carlo steps per site a percolation transition occurs at a concentration distinctly lower than the percolation concentration of the initial random state. This dynamic percolation transition is analyzed with finite-size scaling methods. While at zero temperature, where the system settles down at a frozen-in cluster distribution and further phase separation stops, the critical exponents associated with this percolation transition are consistent with the universality class of random percolation, the critical behavior of the transient time-dependent percolation occurring at nonzero temperature possibly belongs to a different, new universality class.     

Kawasaki dynamics with infinite-range spin exchange

The essential feature of the Kawasaki model is the conserved order parameter, which places the model in class B of the Halperin, Hoheberg, and Ma classification. We have studied the energy relaxation of this model in one and two dimensions with the added feature that spin exchange may take place between any pair of sites within the system. Our results for the dynamic exponentz are indistinguishable from those for class A models, in which the order parameter is not conserved.     

小体积比两相分离早期过程的三维格子气模型研究

采用Monte Carlo模拟方法研究了小体积比三维格子气模型中的相分离过程, 比较了sc, fcc, bcc 等3种晶格类型和T/T_c=0.45–0.85等 5个相对温度的系统演化行为, 计算了系统的结构因子函数, 发现结构因子在相分离早期不满足标度关系, 生长指数等于1/6, 小于经典Lifshitz-Slyozov理论的值. 关键词： 格子气模型 相分离过程 Monte Carlo模拟 生长律     

Finite-size scaling of the three-state Potts model on a simple cubic lattice

Finite-size scaling is studied for the three-state Potts model on a simple cubic lattice. We show that the specific heat and the magnetic susceptibility scale accurately as the volume. The correlation length exhibits behaviors expected for a genuine first-order transition; the one extracted from the unsubtracted correlation function shows a characteristic finite-size behavior, whereas the physical correlation length that characterizes the first excited state stays at a finite value and is discontinuous at the transition point.     

Phase transition in a two-dimensional Ising ferromagnet based on the generalized zero-temperature Glauber dynamics

At zero temperature, based on the Ising model, the phase transition in a two-dimensional square lattice is studied using the generalized zero-temperature Glauber dynamics. Using Monte Carlo （MC） renormalization group methods, the static critical exponents and the dynamic exponent are studied; the type of phase transition is found to be of the first order.     

Scaling behavior of two-dimensional domain growth: Computer simulation of vertex models

Computer simulations are performed for vertex models which are coarse-grained models for dynamical cellular patterns in two dimensions. By simulating large systems, we obtain conclusive evidence of scaling behavior, that is, a power law for the growth of the average cell size and the scaling properties for the distribution functions of edge number and size of cells. Several versions of the vertex models are obtained by making some approximations for the equation of motion of a vertex, and we compare the statistical properties of the patterns in the scaling regime.     

晶格失配对异质外延超薄膜生长中成核特性的影响

利用动力学蒙特卡罗方法模拟了异质外延超薄膜生长中的成核过程.研究了薄膜与衬底的晶格失配对超薄膜生长中成核密度、平均核尺寸、标度关系及生长模式的影响.结果发现产生压（张）应变的晶格负（正）失配使生长过程更早（迟）从成核区进入过渡区，失配越大，这一效应越明显.在相同的沉积条件下，负失配导致超薄膜形成较低的成核密度与较大的平均核尺寸，而正失配则相反.成核密度满足标度关系Ns≈(F/D)χ，随着失配度从-0.04增加到0.02，标度系数χ从0.37逐渐减小到0.33，对应超薄膜生长过程从包含二聚体扩散模式转变到无 关键词： 薄膜生长 成核 晶格失配 蒙特卡罗模拟     

Dynamic Monte Carlo Renormalization group. II

The dynamic Monte Carlo Renormalization group method introduced by Jan, Moseley, and Stauffer is used to determine the dynamic exponent of the Ising model with conserved magnetization in two dimensions. We present an explicit theoretical basis for the method and expand on the original results for the Kawasaki model. The new result clearly demonstrates the validity of the method and the value of the dynamic exponent,z=3.79±0.05, supports the conclusion of Halperin, Hohenberg, and Ma.     

Interface motion in a two-dimensional Ising model with a field

We determine by Monte Carlo simulations the width of an interface between the stable phase and the metastable phase in a two-dimensional Ising model with a magnetic field, in the case of nonconversed order parameter (Glauber dynamics). At zero temperature, the width increases ast with–1/3, as predicted by earlier theories. As temperature increases, the value of the effective exponent that we measure decreases toward the value 1/4, which is the value in the absence of magnetic field.     

Exact and Monte Carlo computations on a lattice model for change of conformation of a polymer

Conformational changes of linear polymers are studied by means of dynamic lattice models. The relaxation rates for the following four parameters describing the conformation of the polymer are studied for various polymer lengths: the square of the end-to-end distance, the square of the radius of gyration, thex component of the end-to-end vector, and the number of windings.In the most realistic models the relaxation rates for the first three of the above-mentioned properties decrease approximately proportional to the square of the number of monomers in agreement with the well-known Rouse model, while the relaxation of the winding number appears to be independent of the polymer length. The long-range interactions due to excluded volume restrictions are found to be of only minor importance compared to the rules presented for the local movements of the polymer segments.The results are obtained by diagonalizing the Markov matrix forn = 3, 4, 5, and 6 and by Monte Carlo simulation forn = 8, 16, 32, 64, and 128, wheren is the number of monomers.     

Effects of Field Orientation on the Driven Lattice Gas

Steady states of the driven lattice gas (DLG) on triangular, hexagonal and square lattices with the field at several fixed orientations to the principal lattice vectors were studied by Monte Carlo simulation. In most cases a strong field suppressed change to a low-temperature ordered phase. On each lattice, one field orientation that caused nonequilibrium ordering was identified. On triangular and hexagonal lattices, dependence of energy and anisotropy on field strength was studied at those orientations. Anisotropic ordering along the field developed at intermediate temperatures under weak fields. Partial ordering along the field persisted to low temperature under strong fields.     

Study of cluster fluctuations in the two-dimensional q-state Potts model

The two-dimensional Potts model with 2 to 10 states is studied using a cluster algorithm to calculate fluctuations in cluster size as well as commonly used quantities like equilibrium averages and the histograms for energy and the order parameter. Results provide information about the variation of cluster sizes depending on the temperature and the number of states. They also give evidence for first-order transition when energy and the order parameter related measurables are inconclusive on small size lattices.     

Two-body correlations and pair formation in the two-dimensional Coulomb gas

We investigate pair correlations in the two-dimensional Coulomb gas made up of two species of point ions carrying electric charges Z₁ e(>0) and Z₂ e(<0), and interaction by the logarithmic Coulomb potential. This system is known to be classically stable for couplings=e ²/k _BTc=2/¦Z₁Z₂¦ (whereT is the temperature). Correlations between equally charged ions are shown to be greatly modified at short distances, in the range _c/2<< _c, due to gradual ion condensation. The usual integral equations for the pair correlation functions admit no solutions in that range. Preliminary Monte Carlo simulations for the symmetric case (Z₁=–Z₂) reveal a striking chemical equilibrium between tightly bound ion pairs and free ions, which is reasonably well described by a simple Bjerrum model.     

二维自旋系统aging现象的数值模拟研究

应用动力学蒙特卡罗模拟方法，对二维Ising模型和二维XY模型的aging现象展开数值研究.系统在零外场条件下从高温无序相淬火到临界温度T_c时，通过测量自关联函数A(t,t′)，观察到二维Ising模型和二维XY模型的aging现象，获得更精确的动力学临界指数λ_c和z的值.特别是对二维XY模型，当初始态为完全无序态时，模拟结果证实存在关于标度行为的对数修正. 关键词： 蒙特卡罗模拟 相变和临界行为 aging现象     

Monte Carlo study of the surface area of liquid droplets

Computer simulation of droplets containingl molecules (l 1000) in a lattice gas shows that the average surface area is proportional tol ; 0.6 in two and = 0.825 in three dimensions for small droplets. These exponents agree approximately with those in Kadanoff's modification of Fisher's droplet model near critical points [= (1 + )/; ourT/T _c is 0.4, 0.7, and 0.9]. For larger droplets, these exponents change to 1/2 (d = 2) and 2/3 (d = 3), the transition occurring for droplet diameters larger than the coherence length and smaller than the critical diameter in the nucleation of supersaturated vapors. This latter result rises some doubts on a recent nucleation theory of Eggingtonet al.     

Dynamical phase transitions in the two-dimensional ANNNI model

We study the phase diagram of the two-dimensional anisotropic next-nearest neighbor Ising (ANNNI) model by comparing the time evolution of two distinct spin configurations submitted to the same thermal noise. We clearly see several dynamical transitions between ferromagnetic, paramagnetic, antiphase, and floating phases. These dynamical transitions seem to occur rather close to the transition lines determined previously in the literature.     

Short-Time Dynamics of Random-Bond Potts Ferromagnet with Continuous Self-Dual Quenched Disorders

We present our Monte Carlo results of the random-bond Potts ferromagnet with the Olson-Young self-dual distribution of quenched disorders in two dimensions. By exploring the short-time scaling dynamics, we find the universal power-law critical behavior of the magnetization and Binder cumulant at the critical point, and thus obtain estimates of the dynamic exponent z and magnetic exponent η, as well as the exponent θ. Our special attention is paid to the dynamic process for the q = 8 Potts model.     

A kinetic Monte Carlo method on super-lattices for the study of the defect formation in the growth of close packed structures

A modified Kinetic Lattice Monte Carlo model has been developed to predict growth rate regimes and defect formation in the case of the homo-epitaxial growth of close packed crystalline structures. The model is an improvement over standard Monte Carlo algorithms, which usually retain fixed atom positions and bond partners indicative of perfect crystal lattices. Indeed, we extend the concepts of Monte Carlo growth simulations on super-lattices containing additional sites (defect sites) with respect to those of the reference material. This extension implies a reconsideration of the energetic mapping, which is extensively presented, and allows to describe a complex phenomenology that is out of accessibility of standard stochastic approaches. Results obtained using the Kawasaki and the Bond-Counting rules for the transition probability of the Monte Carlo event are discussed in details. These results demonstrate how the defect types (local or extended), the formation mechanisms and the defect generation regimes can be characterized using our approach.     

Thermodynamic properties of ternary alloys from Monte Carlo simulations

Methods are presented for obtaining both the integral and partial molar energies, entropies and free energies of the components in rigid ternary substitutional alloy systems from the one Monte Carlo simulation. Tests of the methods for some model systems are presented and discussed.