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

TL;DR

This paper provides an exact analysis of a first order phase transition in the 2D Ising model caused by an inhomogeneous boundary magnetic field, revealing how the transition depends on lattice aspect ratio.

Contribution

It offers an exact determination of the transition line and its dependence on lattice aspect ratio using asymptotic analysis in the thermodynamic limit.

Findings

Identification of the transition line separating localized and propagating interface regimes.

Demonstration of the strong dependence of the critical line on lattice aspect ratio.

Exact asymptotic expansion results for the interfacial free energy.

Abstract

We present in this paper an exact study concerning a first order transition induced by an inhomogeneous boundary magnetic field in the 2D Ising model. From a previous analysis of the interfacial free energy in the discrete case (J. Phys. A, 2849, 2005), we identify, using an asymptotic expansion in the thermodynamic limit, the transition line that separates the regime where the interface is localised near the boundary from the regime where it is propagating inside the bulk. In particular, the critical line has a strong dependence on the aspect ratio of the lattice.