Mean field theory for boundary Ising and tricritical Ising models

TL;DR

This paper applies mean field theory to boundary Ising and tricritical Ising models to qualitatively analyze their phase diagrams, aligning with boundary conformal field theory and contrasting with previous analyses.

Contribution

It provides a mean field theoretical approach to boundary Ising models that agrees with conformal field theory and clarifies discrepancies with prior work.

Findings

Boundary phase diagrams are qualitatively described.

Results agree with boundary conformal field theory.

Contradicts previous analysis by Cappelli et al.

Abstract

Using the technique of mean field theory applied to the lattice boundary Ising and tricritical Ising models we provide a qualitative description of their boundary phase diagrams. We will show this is in agreement with the known picture from boundary conformal field theory and we shall compare our work with that of Cappelli et al and show how their analysis is not in accordance with the physical picture.