Functional renormalization group of the non-linear sigma model and the O(N) universality class

TL;DR

This paper applies the functional renormalization group to the O(N) non-linear sigma model across various dimensions, analyzing its phase structure and critical properties to inform future Monte-Carlo simulations.

Contribution

It introduces a non-perturbative RG approach using a derivative expansion and background field method for the O(N) sigma model in arbitrary dimensions.

Findings

Flow analysis in three dimensions reveals phase structure for different N.

Results provide a reference for Monte-Carlo renormalization group simulations.

Critical properties of the model are characterized across dimensions.

Abstract

We study the renormalization group flow of the O(N) non-linear sigma model in arbitrary dimensions. The effective action of the model is truncated to fourth order in the derivative expansion and the flow is obtained by combining the non-perturbative renormalization group and the background field method. We investigate the flow in three dimensions and analyze the phase structure for arbitrary N. The corresponding results about the critical properties of the models will serve as a reference for upcoming simulations with the Monte-Carlo renormalization group.