Cluster-Spin Gaussian Model for Lattice-Ising Models

Abstract

In this paper we lay special stress on analyzing the topological properties of the lattice systems and try to ovoid the conventional ways to calculate the critical points. Only those clusters with finite sizes can execute the self similar transformations of infinite hierarchies. Each ordered cluster has fractal dimension, their minimum relates to the edge fixed point, which accords with the transformations fixed point relating to a critical point. There are two classes of systems and clusters by their connectivity. Using mathematic mapping method we set up cluster-spin Gaussian model solved accurately. There are single state and -fold coupling state in a reducible cluster, each of which corresponds to a subsystem described by a Gaussian model. By the minimal fractal dimension a final expression of the critical points is obtained. The critical points of three lattice systems are calculated, our method makes the calculations very simplified and highly accurate. A possibility of existence of different clusters at the critical temperature is discussed.