Cluster Identities for the Ising Model as a Basis for Simple Effective Field Approximations Discerning between Various Lattices with the Same Coordination Number

Abstract

Abstract Identities are proposed for clusters of N interacting Ising spins. For a single spin they reduce to Callen identity, for a spin pair to that of Bobák and Jaščur. It is shown that effective field approximations for spin correlations lead to different Curie temperatures for lattices of the same coordination number but different dimension.