Applying the Wang-Landau Algorithm to Lattice Gauge Theory

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.