The Wilson Renormalization Group Approach of the Principal Chiral Model around Two Dimensions

TL;DR

This paper applies the Wilson Renormalization Group method to analyze the Principal Chiral Model near two dimensions, clarifying its universality class and resolving discrepancies in perturbative approaches for frustrated spin systems.

Contribution

It introduces a Renormalization Group analysis of the Principal Chiral Model around two dimensions using the Local Potential Approximation, linking it to the Non-Linear Sigma model universality class.

Findings

Identifies a fixed point in the model consistent with the Non-Linear Sigma model.

Provides insights into the long-distance physics of frustrated spin systems.

Resolves discrepancies between different perturbative methods.

Abstract

We study the Principal Chiral Ginzburg-Landau-Wilson model around two dimensions within the Local Potential Approximation of an Exact Renormalization Group equation. This model, relevant for the long distance physics of classical frustrated spin systems, exhibits a fixed point of the same universality class that the corresponding Non-Linear Sigma model. This allows to shed light on the long-standing discrepancy between the different perturbative approaches of frustrated spin systems.