Scaling relations and multicritical phenomena from Functional Renormalization

TL;DR

This paper uses nonperturbative renormalization group equations to analyze multicritical phenomena in models with competing orders, providing insights into phase diagrams and fixed point stability relevant for quantum phase transitions.

Contribution

It introduces a nonperturbative RG approach to study multicritical points in O(N)+O(M)-models, verifying scaling relations and discussing implications for quantum phase transitions.

Findings

Validated Aharony's scaling relation within the scale-dependent derivative expansion.

Computed stability of isotropic and decoupled fixed points in phase diagrams.

Provided a framework for analyzing multicritical phenomena with truncated flow equations.

Abstract

We investigate multicritical phenomena in O(N)+O(M)-models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To identify possible multicritical points in phase diagrams with two ordered phases, we compute the stability of isotropic and decoupled fixed point solutions from scaling potentials of single-field models. We verify the validity of Aharony's scaling relation within the scale-dependent derivative expansion of the effective average action. We discuss implications for the analysis of multicritical phenomena with truncated flow equations. These findings are an important step towards studies of competing orders and multicritical quantum phase transitions within the framework of Functional Renormalization.