Derivation of low-temperature expansions for Ising model. II. General theory

Abstract

The enumeration problem that arises in the derivation of low‐temperature and high‐field expansions for the Ising model of a ferromagnet and antiferromagnet is studied. The method of partial generating functions (complete codes) is developed and a principle of complete code balance is explicitly stated. The detailed application of the method to a number of lattices is described and substitutions given that interpret the generating functions of certain lattices on the corresponding shadow lattice. It is shown that in zero‐field and two dimensions some of these substitutions reduce to the well‐known star triangle and magnetic‐moment results.