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 3 k -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 .