Exact Sampling for the Ising Model at all Temperatures

TL;DR

This paper presents a polynomial-time method for exact sampling of the Ising model at all temperatures, filling a gap in the literature especially at low temperatures where such results were previously undocumented.

Contribution

The authors introduce a novel technique enabling exact sampling of the Ising model at all temperatures, including low temperatures, which was not previously available in the literature.

Findings

Exact sampling at high temperatures is well-known.

New polynomial-time sampling method for low temperatures.

Survey of mixing times for Glauber dynamics.

Abstract

We give a survey of the known results on mixing time of Glauber dynamics for the Ising model on the square lattice and present a technique that makes exact sampling of the Ising model at all temperatures possible in polynomial time. At high temperatures this is well-known and although this seems to be known also in the low temperature case since Kramer and Waniers paper from the 1950s, we did not found any reference that describes exact sampling for the Ising model at low temperatures.