Recent Results of Multimagnetical Simulations of the Ising Model

TL;DR

This paper uses multimagnetical Monte Carlo simulations to study interfaces in 2D and 3D Ising models, validating methods with 2D results and estimating interfacial tension in 3D.

Contribution

It introduces high-precision multimagnetical simulation techniques for analyzing order interfaces in Ising models, especially in three dimensions.

Findings

High-precision reproduction of 2D exact results

Estimation of critical interfacial tension amplitude in 3D

Validation of numerical methods for interface studies

Abstract

To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the $2D$ and $3D$ Ising model. 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.