Costa Gabriele, Prestipino Santi
Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy.
Entropy (Basel). 2025 Jan 9;27(1):46. doi: 10.3390/e27010046.
Discrete statistical systems offer a significant advantage over systems defined in the continuum, since they allow for an easier enumeration of microstates. We introduce a lattice-gas model on the vertices of a polyhedron called a pentakis icosidodecahedron and draw its exact phase diagram by the Wang-Landau method. Using different values for the couplings between first-, second-, and third-neighbor particles, we explore various interaction patterns for the model, ranging from softly repulsive to Lennard-Jones-like and SALR. We highlight the existence of sharp transitions between distinct low-temperature "phases", featuring, among others, regular polyhedral, cluster-crystal-like, and worm-like structures. When attempting to reproduce the equation of state of the model by Monte Carlo simulation, we find hysteretic behavior near zero temperature, implying a bottleneck issue for Metropolis dynamics near phase-crossover points.
离散统计系统相对于连续统中定义的系统具有显著优势，因为它们允许更轻松地枚举微观状态。我们在一个称为五角化二十面体的多面体顶点上引入了一个晶格气体模型，并通过王-兰道方法绘制了其精确的相图。使用第一、第二和第三近邻粒子之间耦合的不同值，我们探索了该模型的各种相互作用模式，范围从软排斥到类 Lennard-Jones 和 SALR。我们强调了不同低温“相”之间存在尖锐转变，其中包括规则多面体、簇晶状和蠕虫状结构等。当试图通过蒙特卡罗模拟重现该模型的状态方程时，我们发现在零温度附近存在滞后行为，这意味着在相交叉点附近的 metropolis 动力学存在瓶颈问题。
