A numerical method for determining the interface free energy

TL;DR

This paper introduces a numerical method based on the Wang-Landau algorithm to accurately compute free energies and interface tensions in lattice models, demonstrating its effectiveness on the four-state Potts model.

Contribution

The paper presents a novel numerical approach for calculating free energies and interface tensions using the Wang-Landau algorithm, applicable to complex lattice models.

Findings

High-precision determination of the order-order interface tension in the 3D four-state Potts model.

Extraction of infinite volume interface tension from finite volume data.

Numerical evidence supporting perfect wetting at the critical beta.

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 beta 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 the critical value of beta provides a clear numerical evidence of perfect wetting.