The worm algorithm for the Ising model is rapidly mixing

TL;DR

This paper proves that the worm algorithm for the ferromagnetic Ising model mixes rapidly across all finite graphs and temperatures, enabling efficient approximation of key physical quantities.

Contribution

It establishes the rapid mixing property of the worm algorithm for the Ising model on all finite graphs and temperatures, providing a rigorous foundation for approximation schemes.

Findings

Proves rapid mixing of the worm algorithm for all finite graphs and temperatures.

Enables rigorous construction of efficient approximation schemes for Ising susceptibility.

Facilitates accurate computation of two-point correlation functions.

Abstract

We prove rapid mixing of the Prokofiev-Svistunov (or worm) algorithm for the zero-field ferromagnetic Ising model, on all finite graphs and at all temperatures. As a corollary, we show how to rigorously construct simple and efficient approximation schemes for the Ising susceptibility and two-point correlation function.