Introduction to the Propp-Wilson Method of Exact Sampling for the Ising Model

TL;DR

This paper introduces the Propp-Wilson coupling-from-the-past method for the Ising model, allowing exact sampling from equilibrium distributions, and analyzes its efficiency across various parameters.

Contribution

It presents the application of the Propp-Wilson method to the Ising model, including cases with magnetic fields, and studies the coupling time as a measure of ergodic time.

Findings

Coupling time depends on system size, temperature, and field strength.

The method provides exact samples from the equilibrium distribution.

Coupling time estimates ergodic time for the Ising system.

Abstract

An introduction to the Propp-Wilson method of coupling-from-the-past for the Ising model is presented. It enables one to obtain exact samples from the equilibrium spin distribution for ferromagnetic interactions. Both uniform and random quenched magnetic fields are included. The time to couple from the past and its standard deviation are shown as functions of system size, temperature, and the field strength. The time should be an estimate of the ergodic time for the Ising system.