Bailly-Reyre A, Diep H T, Kaufman M
Laboratoire de Physique Théorique et Modélisation Université de Cergy-Pontoise, CNRS, UMR 8089 2, Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042160. doi: 10.1103/PhysRevE.92.042160. Epub 2015 Oct 29.
We study in this paper the phase transition in a mobile Potts model by the use of Monte Carlo simulation. The mobile Potts model is related to a diluted Potts model, which is also studied here by a mean-field approximation. We consider a lattice where each site is either vacant or occupied by a q-state Potts spin. The Potts spin can move from one site to a nearby vacant site. In order to study the surface sublimation, we consider a system of Potts spins contained in a recipient with a concentration c defined as the ratio of the number of Potts spins N(s) to the total number of lattice sites N(L)=N(x)×N(y)×N(z). Taking into account the attractive interaction between the nearest-neighboring Potts spins, we study the phase transitions as functions of various physical parameters such as the temperature, the shape of the recipient, and the spin concentration. We show that as the temperature increases, surface spins are detached from the solid phase to form a gas in the empty space. Surface order parameters indicate different behaviors depending on the distance to the surface. At high temperatures, if the concentration is high enough, the interior spins undergo a first-order phase transition to an orientationally disordered phase. The mean-field results are shown as functions of temperature, pressure, and chemical potential, which confirm in particular the first-order character of the transition.
在本文中，我们通过蒙特卡罗模拟研究了移动Potts模型中的相变。移动Potts模型与稀释Potts模型相关，本文也通过平均场近似对稀释Potts模型进行了研究。我们考虑一个晶格，其中每个格点要么为空，要么被一个q态Potts自旋占据。Potts自旋可以从一个格点移动到附近的空位点。为了研究表面升华，我们考虑一个包含在容器中的Potts自旋系统，其浓度c定义为Potts自旋数N(s)与晶格位点总数N(L)=N(x)×N(y)×N(z)的比值。考虑到最近邻Potts自旋之间的吸引相互作用，我们研究了作为各种物理参数（如温度、容器形状和自旋浓度）函数的相变。我们表明，随着温度升高，表面自旋从固相脱离，在空的空间中形成气体。表面序参量根据到表面的距离表现出不同的行为。在高温下，如果浓度足够高，内部自旋会经历一级相变到取向无序相。平均场结果表示为温度、压力和化学势的函数，这特别证实了相变的一级特征。
