We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide a self-contained introduction to some key ideas and concepts of the field, before discussing three well-known problems: phase transitions in the Ising model, the melting transition on a two-dimensional plane and simulation of an all-atom model for liquid water. We review the classical Metropolis, Glauber and molecular dynamics sampling algorithms before discussing several more recent approaches, including cluster algorithms, novel variations of hybrid Monte Carlo and Langevin dynamics and piece-wise deterministic processes such as event chain Monte Carlo. We highlight cross-over with statistics and machine learning throughout and present some results on event chain Monte Carlo and sampling from the Ising model using tools from the statistics literature. We provide a simulation study on the Ising and XY models, with reproducible code freely available online, and following this we discuss several open areas for interaction between the disciplines that have not yet been explored and suggest avenues for doing so.

翻译：我们讨论统计物理学中未经正常的概率分布抽样的几种算法,但使用统计和机器学习的语言。我们在讨论三个众所周知的问题之前,对该领域的一些关键想法和概念进行自成一体的介绍:Ising模型的阶段过渡、二维平面的融化过渡以及液水全原子模型的模拟。我们审查了古典大都会、Glauber和分子动态抽样算法,然后讨论了最近的一些方法,包括群集算法、混合的Monte Carlo和Langevin动态的新变异以及蒙特卡洛事件链等有碎片的确定论过程。我们强调与整个事件链的统计和机器学习的交叉,并利用统计文献工具对蒙特卡洛事件链和Ising模型的取样工作提出一些结果。我们提供了关于Ising和XY模型的模拟研究,并免费提供在线代码,随后我们讨论了尚未探讨的学科之间互动的若干开放领域,并提出这样做的途径。