Series expansions of the density of states in SU(2) lattice gauge theory

TL;DR

This paper numerically computes the density of states in SU(2) lattice gauge theory, compares it with theoretical expansions, and explores methods to analyze phase transitions via Fisher's zeros.

Contribution

It introduces a numerical approach to calculate the density of states and demonstrates how to improve convergence of expansions for analyzing phase transitions.

Findings

Good overlap of expansions at the crossover region

Logarithmic singularities affect convergence, which can be improved by subtraction

Legendre polynomial expansions may help locate Fisher's zeros

Abstract

We calculate numerically the density of states n(S) for SU(2) lattice gauge theory on $L^4$ lattices. Small volume dependence are resolved for small values of S. We compare $ln(n(S))$ with weak and strong coupling expansions. Intermediate order expansions show a good overlap for values of S corresponding to the crossover. We relate the convergence of these expansions to those of the average plaquette. We show that when known logarithmic singularities are subtracted from $ln(n(S))$, expansions in Legendre polynomials appear to converge and could be suitable to determine the Fisher's zeros of the partition function.