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

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 2α_s = α_b + 2. It follows from scaling relations that in regime III the correlation length exponent νis given by ν=(l+g)/2g, where l is the level and g is the dual Coxeter number. In regime II we find ν=(l+g)/2l.