Microcanonical Determination of the Interface Tension of Flat and Curved Interfaces from Monte Carlo Simulations

TL;DR

This paper uses microcanonical Monte Carlo simulations to accurately determine the interface tension in the 2D q-state Potts model, revealing detailed phase coexistence behavior and finite size effects.

Contribution

It introduces a microcanonical approach with a specialized heatbath algorithm to precisely locate phase transitions and measure interface tension, highlighting the nature of heterophase states.

Findings

Microcanonical ensemble effectively locates first order phase transitions.

Accurate estimates of interface tension are obtained despite finite size effects.

Loop extrema in inverse temperature vs. energy density relate to heterophase states, not spinodal points.

Abstract

The investigation of phase coexistence in systems with multi-component order parameters in finite systems is discussed, and as a generic example, Monte Carlo simulations of the two-dimensional q-state Potts model (q=30) on LxL square lattices (40<=L<=100) are presented. It is shown that the microcanonical ensemble is well-suited both to find the precise location of the first order phase transition and to obtain an accurate estimate for the interfacial free energy between coexisting ordered and disordered phases. For this purpose, a microcanonical version of the heatbath algorithm is implemented. The finite size behaviour of the loop in the curve describing the inverse temperature versus energy density is discussed, emphasizing that the extrema do not have the meaning of van der Waals-like "spinodal points" separating metastable from unstable states, but rather describe the onset of heterophase states: droplet/bubble evaporation/condensation transitions. Thus all parts of these loops, including the parts that correspond to a negative specific heat, describe phase coexistence in full thermal equilibrium. However, the estimates for the curvature-dependent interface tension of the droplets and bubbles suffer from unexpected and unexplained large finite size effects which need further study.