Extracting partition function zeros from Fukui-Todo simulations

TL;DR

This paper introduces a novel reweighting technique and zero-detection protocol to extract partition function zeros from Fukui-Todo simulations, enabling better analysis of critical phenomena in statistical physics models.

Contribution

The paper presents a new method to determine partition function zeros from Fukui-Todo simulations, overcoming previous limitations due to bypassed energy computations.

Findings

Successfully applied to models with first-order transitions

Effective in models with second-order transitions

Enhances understanding of critical phenomena

Abstract

The Fukui-Todo algorithm is an important element of the array of simulational approaches to tackling critical phenomena in statistical physics. The partition-function-zero approach is of fundamental importance to understanding such phenomena and a precise tool to measure their properties. However, because the Fukui-Todo algorithm bypasses sample-by-sample energy computation, zeros cannot easily be harnessed through the energy distribution. Here this obstacle is overcome by a novel reweighting technique and zero-detection protocol. The efficacy of the approach is demonstrated in simple iconic models which feature transitions of both first and second order.