Duality in generalized Ising models

TL;DR

This paper explores duality in generalized Ising models with multi-spin interactions, highlighting a four-dimensional gauge-invariant model that exhibits phases analogous to quark confinement and quark-gluon plasma.

Contribution

It extends previous work on Ising model duality by providing examples and analyzing a 4D gauge-invariant model with implications for quantum chromodynamics.

Findings

Identification of phases with area and perimeter laws for Wilson loops

Connection between Ising model phases and quark confinement phenomena

Analysis of models with multi-spin interactions and their dualities

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.