Universal behavior of coupled order parameters below three dimensions

TL;DR

This paper investigates the universal critical behavior of models with two competing order parameters in dimensions less than or equal to three, revealing complex fixed point structures and multiple universality classes as the dimension approaches two.

Contribution

It introduces novel pseudo-spectral techniques to analyze functional Renormalization Group equations, uncovering intricate fixed point structures in lower dimensions for models with coupled order parameters.

Findings

Exactly one stable fixed point in d=3, indicating bicritical or tetracritical behavior.

Multiple stable fixed points emerge in dimensions approaching 2, suggesting coexistence of universality classes.

New fixed point structures are identified in d<3, enriching the understanding of critical phenomena in coupled systems.

Abstract

We explore universal critical behavior in models with two competing order parameters, and an O(N)+O(M) symmetry for dimensions $d \leq 3$. In d=3, there is always exactly one stable Renormalization Group fixed point, corresponding to bicritical or tetracritical behavior. Employing novel, pseudo-spectral techniques to solve functional Renormalization Group equations in a two-dimensional field space, we uncover a more intricate structure of fixed points in d<3, where two additional bicritical fixed points play a role. Towards d=2, we discover ranges of N=M with several simultaneously stable fixed points, indicating the coexistence of several universality classes.