Free energies and critical exponents of the A_1^{(1)}, B_n^{(1)}, C_n^{(1)} and D_n^{(1)} face models

TL;DR

This paper calculates free energies and critical exponents for integrable models linked to affine Lie algebras, revealing specific scaling relations and expressions for the correlation length exponent in different regimes.

Contribution

It provides explicit formulas for free energies and critical exponents of models associated with elliptic solutions of the star-triangle relation related to affine Lie algebras.

Findings

Bulk and surface specific heat exponents satisfy a scaling relation.

Correlation length exponent f is expressed in terms of level and dual Coxeter number.

Explicit formulas for f in regimes II and III.

Abstract

We obtain the free energies and critical exponents of models associated with elliptic solutions of the star-triangle relation and reflection equation. The models considered are related to the affine Lie algebras A_1^{(1)}, B_n^{(1)},C_n^{(1)} and D_n^{(1)}. The bulk and surface specific heat exponents are seen to satisfy the scaling relation 2\alpha_s = \alpha_b + 2. It follows from scaling relations that in regime III the correlation length exponent \nu is given by \nu=(l+g)/2g, where l is the level and g is the dual Coxeter number. In regime II we find \nu=(l+g)/2l.