Algorithmic Pirogov-Sinai Theory
Obtaining accurate samples from the hard-core model (and related models) is an important problem at the intersection of probability theory, statistical mechanics, and theoretical computer science. I will introduce this problem and describe an algorithm that is efficient at low temperatures on lattices — that is, efficient in precisely the regime in which Glauber dynamics take an exponential time to mix. The algorithm is based on classical tools from statistical mechanics, the cluster expansions and Pirogov-Sinai theory, and Barvinok’s approach to polynomial approximation.
Based on joint work with Will Perkins and Guus Regts.