Structure of interfaces at phase coexistence. Theory and numerics

TL;DR

This paper compares theoretical predictions and Monte Carlo simulations of phase interfaces in the Potts model, revealing distinct interfacial structures below and at critical temperature.

Contribution

It provides a detailed comparison between exact field theory and numerical simulations for phase interfaces in two-dimensional Potts models, confirming key theoretical predictions.

Findings

Below critical temperature, non-boundary colors form drops along a single interface.

At critical temperature for q>4, two interfaces enclose a disordered layer.

Interfacial structures can be distinguished through single-point measurements across system sizes.

Abstract

We compare results of the exact field theory of phase separation in two dimensions with Monte Carlo simulations for the $q$-state Potts model with boundary conditions producing an interfacial region separating two pure phases. We confirm in particular the theoretical predictions that below critical temperature the surplus of non-boundary colors appears in drops along a single interface, while for $q>4$ at critical temperature there is formation of two interfaces enclosing a macroscopic disordered layer. These qualitatively different structures of the interfacial region can be discriminated through a measurement at a single point for different system sizes.