The Physicist's Guide to the HMC

Abstract

The hybrid Monte Carlo (HMC) algorithm is arguably the most efficient sampling method for general probability distributions of continuous variables. Together with exact Fourier acceleration (EFA) the HMC becomes equivalent to direct sampling for quadratic actions $S(x)=\frac{1}{2}{x}^{\mathsf{T}}Mx$ (i.e. normal distributions $x\sim {\mathrm{e}}^{-S(x)}$), only perturbatively worse for perturbative deviations of the action from the quadratic case, and it remains viable for arbitrary actions. In this work the most recent improvements of the HMC including EFA and radial updates are collected into a numerical recipe.

Comments: 9 pages, 3 figures, 4 algorithms; LATTICE2024 proceedings