Applying the Wang-Landau Algorithm to Lattice Gauge Theory
arXiv:0807.1275 · doi:10.1103/PhysRevD.78.074503
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- reduction of SU(N) lattice gauge theories.
40 pages, 13 figures. Added discussions on the way the Wang-Landau algorithm that we use differs from other implementations in the literature, added references, corrected typos, published version
References in corpus (15)
- Escaping free-energy minima
- An efficient, multiple range random walk algorithm to calculate the density of states
- Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
- Understanding and Improving the Wang-Landau Algorithm
- Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
- Wang-Landau algorithm for continuous models and joint density of states
- The density of states method at non-zero chemical potential
- Avoiding Boundary Effects in Wang-Landau Sampling
- Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling
- Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N ?
- Breakdown of large-N quenched reduction in SU(N) lattice gauge theories
- Deconfinement transition in 2+1-dimensional SU(4) lattice gauge theory
- The large-N phase transition of lattice SU(N) gauge theories
- Series expansions of the density of states in SU(2) lattice gauge theory
- Non-Perturbative U(1) Gauge Theory at Finite Temperature