The Markov chain Monte Carlo method as a statistical mechanics technique for the study of macroscopic systems has furnished the scientific community with great knowledge and advances in the theory of phase transitions. While a number of Monte Carlo models have been proposed for the study of surface growth, these models have not nearly being studied as exhaustively as in the models of magnetic systems, a paradigm of which is the classical model of Ernest Ising. In particular, studies of phase transitions in surface/interface science at nanometric scales are almost non-existent. This article has been written to motivate research in this area of statistical mechanics from the perspective of surface science. In this article we survey the rudiments of the method along with some models of disordered systems such as magnetic systems, material fracture, nano-pattern formation under ion bombardment, and molecular chirality. We performed simulations of these models using the method and obtained results that are in excellent agreement with experimental observations.
Tensor Network Markov Chain Monte Carlo: Efficient Sampling of Three-Dimensional Spin Glasses and Beyond
Department of Modern Physics, University of Science and Technology of China（中国科学技术大学近代物理系）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础物理与数学科学学院）
A Monte Carlo Study of the Dipolar Universality Class in Three Dimensions
Graduate School of Science, Osaka Metropolitan University（大阪公立大学理学研究科）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论与数学科学中心（iTHEMS））；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Institut des Hautes Études Scientifiques（高等科学研究所）
