Dynamic critical behavior of the worm algorithm for the Ising model

TL;DR

This paper investigates the dynamic critical behavior of the worm algorithm in simulating 2D and 3D Ising models, revealing a unique three-time-scale autocorrelation pattern and demonstrating slight efficiency advantages over Swendsen-Wang in 3D.

Contribution

It provides new insights into the autocorrelation dynamics of the worm algorithm and compares its efficiency to established methods for the Ising model.

Findings

Autocorrelation functions show a three-time-scale behavior.

Worm algorithm is slightly more efficient than Swendsen-Wang in 3D.

Distinct dynamic critical behavior observed for the worm algorithm.

Abstract

We study the dynamic critical behavior of the worm algorithm for the two- and three-dimensional Ising models, by Monte Carlo simulation. The autocorrelation functions exhibit an unusual three-time-scale behavior. As a practical matter, the worm algorithm is slightly more efficient than Swendsen-Wang for simulating the two-point function of the three-dimensional Ising model.