Surface Free Energies and Surface Critical Behaviour of the ABF Models with Fixed Boundaries, condmat/9511081, to be published in the proceedings of Yang-Baxter Equations and Related Topics

In a previous paper, we introduced re°ection equations for interaction-round-a-face (IRF) models and used these to construct commuting double-row trans-fer matrices for solvable lattice spin models with flxed boundary conditions. In particular, for the Andrews-Baxter-Forrester (ABF) models, we derived special functional equations satisfled by the eigenvalues of the commuting double-row transfer matrices. Here we introduce a generalized inversion rela-tion method to solve these functional equations for the surface free energies. Although the surface free energies depend on the boundary spins we flnd that the associated surface critical exponent fis = (7 ¡ L)=4 is independent of the choice of boundary.