Volume dependence of Fisher's zeros

TL;DR

This paper investigates the distribution of Fisher's zeros in SU(2) lattice gauge theory, comparing different computational methods to identify the most reliable approach for locating these zeros in the complex beta plane.

Contribution

It introduces a combined Chebyshev polynomial and patching method that improves the accuracy of Fisher's zeros estimation in lattice gauge theories.

Findings

Chebyshev-based method yields more reliable zeros

Comparison shows polynomial approximations vary in accuracy

Results enhance understanding of phase transitions in lattice models

Abstract

We study the location of the partition function zeros in the complex beta plane (Fisher's Zeros) for SU(2) lattice gauge theory on L^4 lattices. We discuss recent attempts to locate complex zeros for L=4 and 6. We compare results obtained using various polynomial approximations of the logarithm of the density of states and a straightforward MC reweighting. We conclude that the method based on a combination of discrete Chebyshev orthogonality and patching plaquette distributions at different beta provides the more reliable estimates.