Topological Structures of Cluster Spins for Ising Models
arXiv:1003.3060
Abstract
We discussed hierarchies and rescaling rule of the self similar transformations in Ising models, and define a fractal dimension of an ordered cluster, which minimum corresponds to a fixed point of the transformations. By the fractal structures we divide the clusters into two types: irreducible and reducible. A relationship of cluster spin with its coordination number and fractal dimension is obtained.
7 pages, 3 figures