Exactly Solvable IRF Models. V. A Further New Hierarchy

Abstract

It is shown that a k-state IRF model (σ=0, 1, …, k−1), with a condition k−2≤σ_i+σ_j≤k on adjacent spins σ_i and σ_j, is exactly solvable for all k(k≥3). This proves the existence of a new hierarchy of solvable IRF models. It is also shown that the k-state IRF model is equivalent to a 3k-state solid on solid (SOS) model. Considering all the known results, it is predicted that for an arbitrary set of integers L and f(L≥0, f≥1) there exists a solvable IRF model with the hard core condition L≤σ_i+σ_j≤L+f.