Multicritical behavior in models with two competing order parameters

TL;DR

This paper uses the nonperturbative functional Renormalization Group to analyze multicritical phenomena in models with two competing order parameters, revealing fixed points, stability conditions, and implications for high-energy physics.

Contribution

It provides a comprehensive analysis of fixed points and critical behavior in models with O(N_1)+O(N_2) symmetry, including stability and dimensional transition effects.

Findings

Identification of stable and unstable fixed points in three dimensions.

Evidence of triviality in coupled two-scalar models in high-energy physics.

Discovery of non-canonical critical exponents at semi-Gaussian fixed points.

Abstract

We employ the nonperturbative functional Renormalization Group to study models with an O(N_1)+O(N_2) symmetry. Here, different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the competition of two order parameters. We discuss the critical behavior of the symmetry-enhanced isotropic, the decoupled and the biconical fixed point, and analyze their stability in the N_1, N_2 plane. We study the fate of non-trivial fixed points during the transition from three to four dimensions, finding evidence for a triviality problem for coupled two-scalar models in high-energy physics. We also point out the possibility of non-canonical critical exponents at semi-Gaussian fixed points and show the emergence of Goldstone modes from discrete symmetries.