Sampling from the low temperature Potts model through a Markov chain on flows. Issue 1 (16th April 2022) - Huijben, Jeroen; Patel, Viresh; Regts, Guus
Abstract: In this article, we consider the algorithmic problem of sampling from the Potts model and computing its partition function at low temperatures. Instead of directly working with spin configurations, we consider the equivalent problem of sampling flows. We show, using path coupling, that a simple and natural Markov chain on the set of flows is rapidly mixing. As a result, we find a δ $$ δ $$ ‐approximate sampling algorithm for the Potts model at low enough temperatures, whose running time is bounded by O ( m 2 log ( m δ − 1 ) ) $$ O\left({m}^2\log \left(mδ^{-1}\right)\right) $$ for graphs G $$ G $$ with m $$ m $$ edges.