A Determination of Interface Free Energies

TL;DR

This paper accurately determines the interface free energy between phases in 2D Potts models using multicanonical Monte Carlo simulations, confirming analytical results and clarifying finite-size effects.

Contribution

It provides high-precision numerical estimates of interface free energies in 2D Potts models and challenges previous claims about finite-size correction behavior.

Findings

Results agree with recent analytical calculations.

Energy distribution shows two maxima with 1/L^2 corrections.

Identifies a flat region indicating domain configurations.

Abstract

We determine the interface free energy $F_{o.d.}$ between disordered and ordered phases in the q=10 and q=20 2-d Potts models using the results of multicanonical Monte Carlo simulations on $L^2$ lattices, and suitable finite volume estimators. Our results, when extrapolated to the infinite volume limit, agree to high precision with recent analytical calculations. At the transition point $\beta_t$ the probability distribution function of the energy exhibits two maxima. Their locations have $1/L^2$ corrections, in contradiction with claims of $1/L$ behavior made in the literature. Our data show a flat region inbetween the two maxima which characterizes two domain configurations.