Boundary field induced first-order transition in the 2D Ising model: numerical study

TL;DR

This paper numerically investigates a boundary field-induced first-order transition in the 2D Ising model, confirming theoretical predictions and exploring spin correlations through advanced simulation techniques.

Contribution

It provides numerical validation of the boundary-induced transition and analyzes spin correlations, extending previous analytical work with detailed simulations.

Findings

Interface tension matches theoretical predictions

Identified phase transition point accurately

Explored spin-spin correlations without analytical results

Abstract

In a recent paper, Clusel and Fortin [J. Phys. A.: Math. Gen. 39 (2006) 995] presented an analytical study of a first-order transition induced by an inhomogeneous boundary magnetic field in the two-dimensional Ising model. They identified the transition that separates the regime where the interface is localized near the boundary from the one where it is propagating inside the bulk. Inspired by these results, we measured the interface tension by using multimagnetic simulations combined with parallel tempering to determine the phase transition and the location of the interface. Our results are in very good agreement with the theoretical predictions. Furthermore, we studied the spin-spin correlation function for which no analytical results are available.