Noncommutative Geometry and The Ising Model

TL;DR

This paper explores the interpretation of Ising models as field theories within noncommutative geometry, constructing discrete space models and comparing them with traditional statistical physics models.

Contribution

It introduces a novel framework for modeling Ising-type systems using noncommutative geometry and constructs discrete space field theories with gauge groups.

Findings

Constructed sample models of field theory on discrete spaces

Compared noncommutative geometry models with classical statistical physics models

Developed a discrete gauge theory with a gauge group

Abstract

The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces using the introduced tools of discrete geometry. We write the action for few models, then we compare them with various models of statistical physics. We construct also the gauge theory with a discrete gauge group.