Exact results of a general spin-1 model on 2D decorated lattices

Abstract

By the decoration-iteration transformation, we find a general relation between interaction parameters of a general spin-1 model on any lattice with unique coordination number and on its decorated lattice. We obtain three exact phase transition points of the general spin-1 model on two-dimensional decorated lattices in terms of the exact results of the model on corresponding two-dimensional regular lattices, including the triangle, square, kagome and honeycomb lattices. We find the critical temperatures have no exact relation with the average coordination number and the type of coordination number for both the Ising model and the general spin-1 model.