Surface Free Energies, Interfacial Tensions and Correlation Lengths of the ABF Models

TL;DR

This paper calculates surface free energies, interfacial tensions, and correlation lengths of the ABF models in regimes III and IV, revealing additive interfacial tensions and critical exponents, using transfer matrix and inversion relation methods applicable to other models.

Contribution

It introduces a method to compute surface free energies and interfacial tensions in ABF models, providing explicit critical exponents and demonstrating the additivity of interfacial tensions.

Findings

Interfacial tensions are additive between arbitrary phases.

Critical exponents are derived for regimes III and IV.

Results are obtained using transfer matrix and inversion relation methods.

Abstract

The surface free energies, interfacial tensions and correlation lengths of the Andrews-Baxter-Forrester models in regimes III and IV are calculated with fixed boundary conditions. The interfacial tensions are calculated between arbitrary phases and are shown to be additive. The associated critical exponents are given by $2-\alpha_s=\mu=\nu$ with $\nu=(L+1)/4$ in regime III and $4-2\alpha_s=\mu=\nu$ with $\nu=(L+1)/2$ in regime IV. Our results are obtained using general commuting transfer matrix and inversion relation methods that may be applied to other solvable lattice models.