Properties of Interfaces in the two and three dimensional Ising Model

TL;DR

This paper uses multimagnetical Monte Carlo simulations to study interfaces in 2D and 3D Ising models, accurately estimating interfacial free energies and analyzing probability densities below the Curie point.

Contribution

It provides precise numerical estimates of interfacial tension amplitudes in 3D Ising models and validates methods by reproducing exact 2D results, offering new insights into interface properties.

Findings

Accurate estimation of interfacial tension amplitude in 3D Ising model.

Reproduction of exact 2D results validates the numerical methods.

Analysis of magnetic probability density shape below Curie temperature.

Abstract

To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the $2D$ and $3D$ Ising model. Following Binder we extract the interfacial free energy from the infinite volume limit of the magnetic probability density. Stringent tests of the numerical methods are performed by reproducing with high precision exact $2D$ results. In the physically more interesting $3D$ case we estimate the amplitude $F^s_0$ of the critical interfacial tension $F^s = F^s_0 t^\mu$ to be $F^s_0 = 1.52 \pm 0.05$. This result is in good agreement with a previous MC calculation by Mon, as well as with experimental results for related amplitude ratios. In addition, we study in some details the shape of the magnetic probability density for temperatures below the Curie point.