Applying the Wang-Landau Algorithm to Lattice Gauge Theory

TL;DR

This paper applies an enhanced Wang-Landau algorithm to SU(N) lattice gauge theories, accurately determining the phase transition point and supporting the validity of large-N reduction.

Contribution

The authors introduce a variant of the Wang-Landau algorithm with continuous fluctuations, enabling precise density of states calculations for large N lattice gauge theories.

Findings

Identified the coupling lambda_t for the first order transition at large N.

Achieved agreement with multi-histogram reweighting within 0.2%.

Extrapolated results to N=∞, finding 1/lambda_t = 0.3148(2).

Abstract

We implement the Wang-Landau algorithm in the context of SU(N) lattice gauge theories. We study the quenched, reduced version of the lattice theory and calculate its density of states for N=20,30,40,50. We introduce a variant of the original algorithm in which the weight function used in the update does not asymptote to a fixed function, but rather continues to have small fluctuations which enhance tunneling. We formulate a method to evaluate the errors in the density of states, and use the result to calculate the dependence of the average action density and the specific heat on the `t Hooft coupling lambda. This allows us to locate the coupling lambda_t at which a strongly first order transition occurs in the system. For N=20 and 30 we compare our results to those obtained using Ferrenberg-Swendsen multi-histogram reweighting and find agreement with errors of 0.2 % or less. Extrapolating our results to N=oo we find 1/lambda_t = 0.3148(2). We remark on the significance of this result for the validity of quenched large-$N$ reduction of SU(N) lattice gauge theories.