The worm process for the Ising model is rapidly mixing

TL;DR

This paper proves that the worm process for the ferromagnetic Ising model mixes rapidly on all finite connected graphs at any temperature, enabling efficient approximation of key physical quantities.

Contribution

It establishes the rapid mixing property of the worm process for the Ising model across all graphs and temperatures, which was previously unknown.

Findings

Rapid mixing of the worm process on all finite connected graphs

Development of a fully-polynomial randomized approximation scheme for the Ising susceptibility

Efficient approximation of the two-point correlation function in the ferromagnetic Ising model

Abstract

We prove rapid mixing of the worm process for the zero-field ferromagnetic Ising model, on all finite connected graphs, and at all temperatures. As a corollary, we obtain a fully-polynomial randomized approximation scheme for the Ising susceptibility, and for a certain restriction of the two-point correlation function