The Classification of Certain Four-Weight Spin Models

Abstract.

In this paper we show that if one of the matrices {W _i , 1 ≤i≤ 4} of a four-weight spin model (X, W ₁ , W ₂ , W ₃ , W ₄ ; D) is equivalent to the matrix of a Potts model or a cyclic model as type II matrix and |X|≥ 5, then the spin model is gauge equivalent to a Potts model or a cyclic model up to simultaneous permutations on rows and columns. Using this fact and Nomura's result [12] we show that every four-weight spin model of size |X|= 5 is gauge equivalent to either a Potts model or a cyclic model up to simultaneous permutations on rows and columns.