Universality classes of three-dimensional $mn$-vector model

TL;DR

This paper investigates the critical behavior of the three-dimensional $mn$-vector model, identifying conditions under which it diverges from the spherically symmetric universality class using advanced renormalization group techniques.

Contribution

It provides a detailed analysis of the phase diagram and universality classes of the 3D $mn$-vector model through high-order perturbative renormalization group calculations.

Findings

Identifies parameter regions with different universality classes.

Maps the phase diagram of the $mn$-vector model.

Determines conditions for non-spherical critical behavior.

Abstract

We study the conditions under which the critical behavior of the three-dimensional $mn$-vector model does not belong to the spherically symmetrical universality class. In the calculations we rely on the field-theoretical renormalization group approach in different regularization schemes adjusted by resummation and extended analysis of the series for renormalization-group functions which are known for the model in high orders of perturbation theory. The phase diagram of the three-dimensional $mn$-vector model is built marking out domains in the $mn$-plane where the model belongs to a given universality class.