A New Family of Solvable Lattice Models Associated with $A_{n}^{(1)}$

Abstract

Presented is a new family of solvable solid-on-solid models in two-dimensional statistical mechanics. The site variables take the values in a set of not necessarily dominant integral weights of the affine Lie algebra $A^{(1)}_n$. The local state probabilities are obtained and the critical behavior is studied. Our family gives an extension of some recently discovered hierarchies of solvable solid-on-solid models.