Critical behavior of classical spin models and local cohomology

TL;DR

This paper links the critical points of classical spin models to local cohomology classes and Noether currents, providing a new mathematical perspective on phase transitions using reflection positivity.

Contribution

It introduces a novel connection between critical phenomena in spin models and local cohomology, advancing the theoretical understanding of phase transitions.

Findings

Critical points correspond to trivial local cohomology classes.

A relation between critical point location and autocorrelation functions.

Use of reflection positivity as a key analytical tool.

Abstract

Using reflection positivity as the main tool, we establish a connection between the existence of a critical point in classical spin models and the triviality of a certain local cohomology class related to the Noether current of the model in the continuum limit. Furthermore we find a relation between the location of the critical point and the momentum space autocorrelation function of the Noether current.