A self dual relation for a three dimensional assembly

Abstract

An Ising model, which is defined on a face centred cubic lattice in which nearest neighbour spins are coupled via a special four spin coupling term involving the 4-point simplex subgraphs of the lattice, is shown to have a self dual property of the type originally put forward by Onsager for the conventional square net Ising model problem. Assuming that this model has one and only one critical point, the location of the singularity can be determined exactly.