Critical Slowing Down of Cluster Algorithms for Ising Models Coupled to 2-d Gravity

TL;DR

This paper investigates the critical slowing down in cluster algorithms for Ising models coupled to 2D gravity, highlighting the impact of local triangulation and baby universes on autocorrelation times.

Contribution

It demonstrates the significant critical slowing down in cluster algorithms for Ising models on 2D gravity and links it to the local nature of the triangulation process.

Findings

Critical slowing down observed, especially in magnetization.

Autocorrelation times increase due to baby universe formation.

Local triangulation algorithms hinder cluster growth.

Abstract

We simulate single and multiple Ising models coupled to 2-d gravity using both the Swendsen-Wang and Wolff algorithms to update the spins. We study the integrated autocorrelation time and find that there is considerable critical slowing down, particularly in the magnetization. We argue that this is primarily due to the local nature of the dynamical triangulation algorithm and to the generation of a distribution of baby universes which inhibits cluster growth.