Reduced critical slowing down for statistical physics simulations

TL;DR

This paper introduces a method to reduce critical slowing down in statistical physics simulations by selecting the slow mode as a collective coordinate, demonstrated on the Ising model with significant improvements over local updates.

Contribution

The paper proposes a novel approach to mitigate critical slowing down by choosing the slow mode for collective integration, showing substantial reductions in autocorrelation times.

Findings

Super critical slowing down observed with heatbath algorithms.

Using magnetization as collective coordinate reduces slowing down.

Autocorrelation times grow polynomially, not exponentially, with system size.

Abstract

Wang-Landau simulations offer the possibility to integrate explicitly over a collective coordinate and stochastically over the remainder of configuration space. We propose to choose the so-called "slow mode", which is responsible for large autocorrelation times and thus critical slowing down, for collective integration. We study this proposal for the Ising model and the linear-log-relaxation (LLR) method as simulation algorithm. We firstly demonstrate super critical slowing down in a phase with spontaneously broken symmetry and for the heatbath algorithms, for which autocorrelation times grow exponentially with system size. By contrast, using the magnetisation as collective coordinate, we present evidence that super critical slowing down is absent. We still observe a polynomial increase of the autocorrelation time with volume (critical slowing down), which is however reduced by orders of magnitude when compared to local update techniques.