Numerical method for determining the interface free energy

Abstract

We propose a general method (based on the Wang-Landau algorithm) to compute numerically free energies that are obtained from the logarithm of the ratio of suitable partition functions. As an application, we determine with high accuracy the order-order interface tension of the four-state Potts model in three dimensions on cubic lattices of linear extension up to L = 56. The infinite volume interface tension is then extracted at each β from a fit of the finite volume interface tension to a known universal behavior. A comparison of the order-order and order-disorder interface tension at βc provides a clear numerical evidence of perfect wetting.

Density of States in Gauge Theories

“…The density of states is calculated for a SU(2) and a compact U(1) lattice gauge theory using a modified version of the Wang-Landau algorithm. We find that the density of states of the SU(2) gauge theory can be reliably calculated over a range of 120,000 orders of magnitude for lattice sizes as big as 20 4 . We demonstrate the potential of the algorithm by reproducing the SU(2) average action, its specific heat and the critical couplings of the weak first order transition in U(1).…”

“…To date, the method has found various applications in Statistical Mechanics, some of which have produced remarkable results that can not be obtained with a direct Monte-Carlo approach (see e.g. [4] for a recent example). Despite its popularity in Statistical Mechanics, the Wang-Landau algorithm has found only limited applications in Lattice Gauge Theory [5,6].…”

Interface tension of 3d 4-states Potts model using the Wang-Landau algorithm

“…A fit of the date according to Eq. (4.4) yields 2σ do = 0.0252 (4). The insertion of a term c 3 /L 3 in the fitting function, justified by the use of the estimator (4.3), gives a compatible result.…”

“…A fit with 9 degrees of freedom has χ 2 /9 = 0.11. The values are σ oo = 0.0249(6) and ρ = 0.76 (4). See the right panel of Fig.…”

“…In [4] we have proposed a new method to calculate interface tensions. It is based on the Wang-Landau [5] algorithm.…”