Interacting N-vector order parameters with O(N) symmetry

TL;DR

This paper investigates the critical behavior of systems with two N-vector order parameters under O(N) symmetry, revealing conditions for multicritical transitions with enlarged symmetries and identifying specific fixed points for N=2, 3, 4.

Contribution

It characterizes the conditions under which multicritical transitions with enhanced symmetry occur in systems with two N-vector order parameters, extending understanding of their critical behavior.

Findings

Multicritical transition with O(2)xO(N) symmetry identified.

Fixed points associated with the mn model for N=2, 3, 4.

Symmetry enlargement at critical points to [SO(N)+SO(N)]xC_2.

Abstract

We consider the critical behavior of the most general system of two N-vector order parameters that is O(N) invariant. We show that it may a have a multicritical transition with enlarged symmetry controlled by the chiral O(2)xO(N) fixed point. For N=2, 3, 4, if the system is also invariant under the exchange of the two order parameters and under independent parity transformations, one may observe a critical transition controlled by a fixed point belonging to the mn model. Also in this case there is a symmetry enlargement at the transition, the symmetry being [SO(N)+SO(N)]xC_2, where C_2 is the symmetry group of the square.