Duality in generalized Ising models

Abstract

This paper rests to a large extend on a paper I wrote some time ago on 'Duality in generalized Ising models and phase transitions without local order parameter'. It deals with Ising models with interactions containing products of more than two spins. In contrast to the old paper I will first give examples before I come to the general statements. Of particular interest is a gauge invariant Ising model in four dimensions. It has important properties in common with models for quantum chromodynamics as developed by Ken Wilson. One phase yields an area law for the Wilson-loop yielding an interaction increasing proportional to the distance and thus corresponding to quark-confinement. The other phase yields a perimeter law allowing for a quark-gluon plasma.