Fisher's zeros of quasi-Gaussian densities of states

TL;DR

This paper investigates the zeros of the partition function in complex parameter space for SU(2) lattice gauge theory, proposing new criteria and methods to identify and analyze Fisher's zeros, especially when the density of states is nearly Gaussian.

Contribution

It introduces a new criterion for the reliable region of reweighting methods and new techniques to detect Fisher's zeros outside this region in lattice gauge theories.

Findings

Proposed a criterion for trustworthy reweighting regions.

Developed methods to infer zeros outside the Gaussian region.

Validated methods using quasi-Gaussian Monte Carlo distributions.

Abstract

We discuss apparent paradoxes regarding the location of the zeros of the partition function in the complex $\beta$ plane (Fisher's zeros) of a pure SU(2) lattice gauge theory in 4 dimensions. We propose a new criterion to draw the region of the complex $\beta$ plane where reweighting methods can be trusted when the density of states is almost but not exactly Gaussian. We propose new methods to infer the existence of zeros outside of this region. We demonstrate the reliability of these proposals with quasi Gaussian Monte Carlo distributions where the locations of the zeros can be calculated by independent numerical methods. The results are presented in such way that the methods can be applied for general lattice models. Applications to specific lattice models will be discussed in a separate publication.