Critical and multicritical behavior in the Ising-Heisenberg universality class

TL;DR

This paper investigates the critical behavior of frustrated antiferromagnets with collinear spin order, revealing first-order transitions for most cases and a potential second-order transition for Ising spins, using renormalization group analysis and Monte Carlo simulations.

Contribution

It introduces a new universality class for frustrated antiferromagnets with specific symmetry breaking, combining analytical and numerical methods to characterize phase transitions.

Findings

First-order transitions for N=2,3 in all models.

Potential second-order transition for Ising spins (N=1).

Exclusion of second-order or pseudo-first order transitions for N=1.

Abstract

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang-Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N=1,2,3 and in all of them find a first-order transition. For the N=1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.