Surface phase transitions of multiple-site associating fluids

Surface phase transitions of Lennard–Jones (LJ) based two- and four-site associating fluids have been studied for various associating strengths using grand-canonical transition matrix Monte Carlo simulations. Our results suggest that, in the case of a smooth surface, represented by a LJ 9-3-type potential, multiple-site associating fluids display a prewetting transition within a certain temperature range. However, the range of the prewetting transition decreases with increasing associating strength and increasing number of sites on the fluid molecules. With the addition of associating sites on the surface, a quasi-2D vapor–liquid transition may appear, which is observed at a higher surface site density for weaker associating fluids. The prewetting transition at lower associating strength is found to shift towards the quasi-2D vapor–liquid transition with increasing surface site density. However, for highly associating fluids, the prewetting transition is still intact, but shifts slightly towards the lower temperature range. Adsorption isotherms, chemical potentials and density profiles are used to characterize surface phase transitions.     

Determination of the vapor–liquid transition of square-well particles using a novel generalized-canonical-ensemble-based method

The square-well(SW) potential is one of the simplest pair potential models and its phase behavior has been clearly revealed, therefore it has become a benchmark for checking new theories or numerical methods. We introduce the generalized canonical ensemble(GCE) into the isobaric replica exchange Monte Carlo(REMC) algorithm to form a novel isobaric GCE-REMC method, and apply it to the study of vapor–liquid transition of SW particles. It is validated that this method can reproduce the vapor–liquid diagram of SW particles by comparing the estimated vapor–liquid binodals and the critical point with those from the literature. The notable advantage of this method is that the unstable vapor–liquid coexisting states,which cannot be detected using conventional sampling techniques, are accessed with a high sampling efficiency. Besides,the isobaric GCE-REMC method can visit all the possible states, including stable, metastable or unstable states during the phase transition over a wide pressure range, providing an effective pathway to understand complex phase transitions during the nucleation or crystallization process in physical or biological systems.     

Phase transitions of bilayer spin-1/2 Baxter-Wu model with repulsive interlayer interactions

Using a Monte Carlo simulation and the single histogram reweighting technique, we study the critical behaviors and phase transitions of the Baxter-Wu model on a two-layer triangular lattice with repulsive interlayer interactions. Via the finite-size analysis, we obtain the transition temperatures and critical exponents at different interlayer coupling strengths. The reduced energy cumulants and the histograms reveal pseudo-first-order phase transitions, and the critical exponents derivate from the standard Baxter-Wu model if the coupling is weak. As the increase of the coupling, the behavior of the pseudo-first order transition disappears and the critical exponents are in accordance with the ones known for the 2D 4-state Potts model.     

Nonequilibrium dynamical phase transition of 3D kinetic Ising／Heisenberg spin system

We have studied the nonequilibrium dynamic phase transitions of both three-dimensional (3D) kinetic Ising and Heisenberg spin systems in the presence of a perturbative magnetic field by Monte Carlo simulation. The feature of the phase transition is characterized by studying the distribution of the dynamical order parameter. In the case of anisotropic Ising spin system (ISS), the dynamic transition is discontinuous and continuous under low and high temperatures respectively, which indicates the existence of a tri-critical point (TCP) on the phase boundary separating low-temperature order phase and high-temperature disorder phase. The TCP shifts towards the higher temperature region with the decrease of frequency, i.e. T_{TCP}=1.33×exp(-ω/30.7). In the case of the isotropic Heisenberg spin system (HSS), however, the situation on dynamic phase transition of HSS is quite different from that of ISS in that no stable dynamical phase transition was observed in kinetic HSS after a threshold time. The evolution of magnetization in the HSS driven by a symmetrical external field after a certain duration always tends asymptotically to a disorder state no matter what an initial state the system starts with. The threshold time τ depends upon the amplitude H_{0}, reduced temperature T/T_C and the frequency ω as τ=C·ω^α·H_0^{-β}·(T/T_C)^{-γ}.     

方阱链流体在固液界面分布的密度泛函理论研究

应用Yethiraj的加权密度近似泛函理论研究平板狭缝中方阱链流体的密度分布，系统的Helm holtz自由能泛函分为理想气体的贡献利剩余贡献两部分，其中剩余贡献部分分别采用刘洪 来等人建立的基于空穴相关函数的方阱链流体状态方程和Gil-Villegas等人提出的统计缔合 流体理论状态方程(SAFT-VR)结合简单加权密度近似计算.考察了不同链长、温度、系统密度 和壁面吸引强度下平板狭缝中方阱链流体的密度分布，并与Monte Carlo(MC)模拟结果进行 了比较.结果表明采用不同的状态方程对密度分布的计算有明显的影响，对于受限于硬壁狭 缝中的方阱链流体，温度和密度比较高时，两种状态方程计算的结果均与MC模拟符合得比较 好，在低温和低密度下效果变差，SAFT-VR方程的计算结果更接近于MC模拟结果.对于受限于 方阱壁狭缝中的方阱链流体，由于系统密度分布的非均匀性加强，采用两种状态方程计算的 结果均与MC模拟结果有一定偏差，寻找更合适的权重函数是进一步改进的关键. 关键词： 密度泛函理论 非均匀流体 密度分布 固液界面 方阱链     

Phase transitions of two spin-1/2 Baxter–Wu layers coupled with Ising-type interactions

Using a Monte Carlo simulation and the single histogram reweighting technique,we study the critical behaviors and phase transitions of the Baxter-Wu(BW)model on a two-layer triangular lattice with Ising-type interlayer couplings.Via the finite-size analysis,we obtain the transition temperatures and critical exponents at repulsive and attractive interlayer couplings.The data for the repulsive interlayer coupling suggest continuous transitions,and the critical behaviors are the same as those of the 2D BW model,belonging to the four-state Potts universality class.The reduced energy cumulants and the histograms reveal that attractive coupling leads to weak firstorder phase transitions.The pseudocritical exponents with the existence of the interlayer couplings indicate that the first-order transition is very close to the critical point of the 2D standard BW model.     

非均匀基底上三维薄膜生长的模拟研究

考虑原子在基底表面的扩散、沿岛周界的扩散和不同层间的扩散以及非均匀基底上表面吸附能分布的各向异性，建立起非均匀基底表面上原子扩散和三维薄膜生长的动力学蒙特卡罗模型.模拟得到在不同生长条件下出现的层状生长、岛状生长和混合生长三种生长模式和相应的多层薄膜生长形貌图.通过统计三维薄膜中原子在各层的分布，计算薄膜的表面粗糙度，得到薄膜生长模式与生长条件之间的关系. 关键词： 薄膜生长 非均匀基底 动力学蒙特卡罗模拟     

Employment, Production and Consumption model: Patterns of phase transitions

We have simulated the model of Employment, Production and Consumption (EPC) using Monte Carlo. The EPC model is an agent based model that mimics very basic rules of industrial economy. From the perspective of physics, the nature of the interactions in the EPC model represents multi-agent interactions where the relations among agents follow the key laws for circulation of capital and money. Monte Carlo simulations of the stochastic model reveal phase transition in the model economy. The two phases are the phase with full unemployment and the phase with nearly full employment. The economy switches between these two states suddenly as a reaction to a slight variation in the exogenous parameter, thus the system exhibits strong non-linear behavior as a response to the change of the exogenous parameters.     

无序杂质区域对沉积在胶体基底表面的金原子凝聚体分形结构的影响

由于受基底表面无规分布杂质的影响,沉积在熔融玻璃基底表面的金原子凝聚形成了具有特殊结构的分形凝聚体.根据这一实验结果,建立了各向异性的团簇团簇凝聚模型,对此类胶体基底表面的金原子分枝状凝聚体的生长过程进行了计算机模拟,研究了无规分布的杂质区域对凝聚体各种参数的影响,其结果与实验相符合 关键词： 薄膜生长 MonteCarlo模拟 分形     

Phase transitions and universality in nonequilibrium steady states of stochastic Ising models

We present results of direct computer simulations and of Monte Carlo renormalization group (MCRG) studies of the nonequilibrium steady states of a spin system with competing dynamics and of the voter model. The MCRG method, previously used only for equilibrium systems, appears to give useful information also for these nonequilibrium systems. The critical exponents are found to be of Ising type for the competing dynamics model at its second-order phase transitions, and of mean-field type for the voter model (consistent with known results for the latter).     

非均质基底表面上团簇生长的Monte Carlo模拟

Monte Carlo方法模拟了在非均质基底表面上团簇的生长过程.非均质基底由规则分布的A，B两类不同性质的物质(不同材料、不同温度等)组成.沉积粒子的初动能为E₀，在不同相基底上单位长度扩散的能耗为E_A,E_B，粒子从A经过相界扩散到B的能耗为E_AB.模拟中粒子的初动能E₀.远大于E_A,E_B，粒子从B过相界到A能耗E_BA取为0.结果表明，沉积在此类基底表面的粒子凝聚成具有分形结构的团簇.当E_AB远大于E_A,E_B时，团簇的数目、团簇的回旋半径、团簇的分形维数均随E₀/E_AB呈周期性变化. 关键词： 分形团簇 非均质基底 Monte Carlo模拟 周期性     

On the Euler characteristics of random surfaces

In a Monte Carlo computer experiment, we simulate the Gibbs distribution of nonconnected two-dimensional surfaces isometrically embedded in three-dimensional Euclidean space with fixed boundary and the action given by the area. The simulation involves surfaces built out of plaquettes in a cubical lattice. The foam structure is analyzed in terms of correlations of the local fluctuations in the Euler characteristic and the area. The scaling behavior of the area and the Euler characteristic is discussed by varying the boundary. We show evidence of a phase transition point which is independent of the choice of the boundary. An existence proof is given of the thermodynamic limit for the models considered.Supported in part by the Deutsche Forschungsgemeinschaft and NSF grant No. Phy 81 09110A 01.     

EFFECTS OF ISLAND-EDGE EXCHANGE BARRIER ON 2D PATTERN FORMATION IN SURFACTANT-MEDIATED EPITAXY

The nucleation and growth of two-dimensional islands in a surfactant-mediated epitaxy system have been studied by computer simulation. To improve the recent results published in the literature, we use a configuration-dependent energy barrier for the exchange process at the island edge in our model. The simulations produce fractal islands at high temperatures or low deposition fluxes, and a transition to regular compact islands occurs at lower temperatures or higher fluxes, in good agreement with the recent experimental results. The barrier for the island-edge exchange has quite a strong effect on the island density as a function of temperature and flux. A small change of the island-edge exchange barrier induces a large variation of the island density in the low-temperature or high-flux region. The flux-dependent island density shows a clear scaling-law behaviour in the intermediate-flux region. The scaling exponent increases evidently as the island-edge exchange barrier increases.     

Majority-vote model with a bimodal distribution of noises

We consider the majority-vote dynamics where the noise parameter, associated with each spin on a two-dimensional square lattice, is a bimodally distributed random variable defined as q$q$ with probability (1−f)$(1-f)$ or zero with probability f$f$, where 0≤f≤1$0\le f\le 1$ is the proportion of noiseless sites. We use Monte Carlo simulations and finite size scaling theory to characterize the ordered and disordered phases and study the phase transition of the model. We conclude that in the thermodynamic limit, the value of the critical noise below which there exists an ordered phase increases with f$f$, the fraction of sites with zero noise. The calculation of the critical exponents shows that the introduction of disorder in the noise parameter does not alter the Ising critical behavior of the model system.     

First-order transition in a 2D classical XY-model using microcanonical Monte Carlo simulations

We have simulated two-dimensional classical XY-model in a microcanonical ensemble using the Monte Carlo technique. Simulations were carried out on a square lattice having 25, 100 or 900-spins with periodic boundary conditions. The nearest neighbour interaction potential was taken to beV(θ)=2J[1−cos¹⁰⁰(θ/2)]. The system energy, mean square magnetization and vortex-density were calculated as functions of temperature. A sudden change in the system energy, vortex density and mean square magnetization was observed at the first-order transition which is associated with this choice of the nearest neighbour interaction potential. The transition temperature increases with decrease in the system size. It is found that the creation of a vortex-antivortex pair costs more energy during the first-order transition than the energy associated with a tightly bound vortex-antivortex pair.     

Monte Carlo Investigation of Adsorption Stage of O on Ru（0001）：a Study of a Lattice Model

The adsorption of O on Ru(0001) is studied by means of Monte Carlo simulation of lattice gas model on a triangular lattice. A recent STM study shows that at low coverage the p(2×2) structure grows via island formation but the p(2×1) structure is abruptly formed at a critical coverage. Moreover, it also shows that there is a coexistence of the p(2×2) and p(2×1) structures. The above results seem not to coincide with the former studies of the system by both the LEED and Monte Carlo simulation. We therefore carried out the Monte Carlo study for the system again in the present paper and found that our simulation almost agrees with the results of the STM.