Apparent first-order wetting and anomalous scaling in the two-dimensional Ising model

TL;DR

This paper provides an exact analysis of wetting transitions in the 2D Ising model, revealing a critical-to-first-order transition shift and anomalous scaling behavior in a pre-asymptotic regime.

Contribution

It introduces an exact calculation of the phase diagram including surface effects and uncovers anomalous scaling in the wetting transition.

Findings

Wetting transition is second order for finite surface coupling ratios.

Transition becomes first order as surface coupling ratio approaches infinity.

Anomalous scaling with exponent 3/2 occurs in a pre-asymptotic regime.

Abstract

The global phase diagram of wetting in the two-dimensional (2d) Ising model is obtained through exact calculation of the surface excess free energy. Besides a surface field for inducing wetting, a surface-coupling enhancement is included. The wetting transition is critical (second order) for any finite ratio of surface coupling J_s to bulk coupling J, and turns first order in the limit J_s/J to infinity. However, for J_s/J much larger than 1 the critical region is exponentially small and practically invisible to numerical studies. A distinct pre-asymptotic regime exists in which the transition displays first-order character. Surprisingly, in this regime the surface susceptibility and surface specific heat develop a divergence and show anomalous scaling with an exponent equal to 3/2.