Lattice models in statistical mechanics for N = 2 superconformal field theory

We study exactly solvable cyclic solid-on-solid models extended to arbitrary higher degrees of the fusion construction. A detailed calculation of their local state probabilities via the corner transfer matrix method is presented. The order parameters thus obtained include new characters of the conformal field theories. We discuss a series of lattice analogues of the N = 2 superconformal minimal models included in this family of the cyclic solid-on-solid models.