A polymer model equivalent to the Ising model

Abstract

It is shown that the zero-field Ising model is equivalent to a polymer model in which a bond of a polymer chain can assume one gauche and one trans state. The Ising model is defined on a lattice graph G of degree d=4, whereas the polymer model is defined on a covering lattice digraph D^c of out-degree d*=2. As an example, a polymer model, defined on the Manhattan square lattice, is shown to be equivalent to the zero-field Ising model on the square lattice. The polymer model can be used to discuss the melting transition in polymers.