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We discuss several algorithms for sampling from unnormalized probabilitydistributions in statistical physics, but using the language of statistics andmachine learning. We provide a self-contained introduction to some key ideasand concepts of the field, before discussing three well-known problems: phasetransitions in the Ising model, the melting transition on a two-dimensionalplane and simulation of an all-atom model for liquid water. We review theclassical Metropolis, Glauber and molecular dynamics sampling algorithms beforediscussing several more recent approaches, including cluster algorithms, novelvariations of hybrid Monte Carlo and Langevin dynamics and piece-wisedeterministic processes such as event chain Monte Carlo. We highlightcross-over with statistics and machine learning throughout and present someresults on event chain Monte Carlo and sampling from the Ising model usingtools from the statistics literature. We provide a simulation study on theIsing and XY models, with reproducible code freely available online, andfollowing this we discuss several open areas for interaction between thedisciplines that have not yet been explored and suggest avenues for doing so.

Sampling algorithms in statistical physics: a guide for statistics and machine learning