Applying the Wang-Landau algorithm to lattice gauge theory
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 that 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 λ. This allows us to locate the coupling λt at which a strongly first-order transition occurs in the system. For N=20 and 30 we compare our results with those obtained using Ferrenberg-Swendsen multihistogram reweighting and find agreement with errors of 0.2% or less. Extrapolating our results to N=∞, we find (λt)-1=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.
- Publication:
-
Physical Review D
- Pub Date:
- October 2008
- DOI:
- 10.1103/PhysRevD.78.074503
- arXiv:
- arXiv:0807.1275
- Bibcode:
- 2008PhRvD..78g4503B
- Keywords:
-
- 11.15.Ha;
- 11.15.Pg;
- 12.38.Gc;
- Lattice gauge theory;
- Expansions for large numbers of components;
- Lattice QCD calculations;
- High Energy Physics - Lattice;
- Condensed Matter - Statistical Mechanics;
- Physics - Computational Physics
- E-Print:
- 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