Continuous Local Symmetry in Ising-type Models

TL;DR

This paper explores a class of generalized Ising models to identify a low energy sector featuring Dirac fermions coupled to Yang-Mills vectors, using covariant gap equations related to crystallographic space groups.

Contribution

It introduces a novel approach employing covariant gap equations to analyze generalized Ising models with symmetry considerations.

Findings

Identification of a low energy sector with Dirac fermions

Coupling of fermions to Yang-Mills vectors

Use of crystallographic space group symmetry in gap equations

Abstract

A class of generalized Ising models is examined with a view to extracting a low energy sector comprising Dirac fermions coupled to Yang-Mills vectors. The main feature of this approach is a set of gap equations, covariant with respect to one of the $4$-dimensional crystallographic space groups.