  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.
