Solvable lattice models with minimal and nonunitary critical behaviour in two dimensions

The exact local height probabilities found by Forrester and Baxter for a series of solvable lattice models in two dimensions are written in terms of nonunitary Virasoro characters and modifications of unitary A1(1) affine Lie algebra characters directly related to nonunitary but rational-level A1(1) characters. The relation between these results and a rational-level GKO decomposition is given. The off-critical lattice origin of the Virasoro characters and the role of the embedding diagram null vectors in the CTM eigenspace is described. Suggestions for the definition of rational and nonunitary models corresponding to arbitrary G/H cosets are given. (orig.)