Crossover from $O(3)$ to $O(4)$ behavior in weakly frustrated antiferromagnets

TL;DR

This paper studies how weak frustration in antiferromagnets causes a crossover from O(3) to O(4) critical behavior, revealing a transition influenced by incommensurability and temperature effects.

Contribution

It extends the CP^1 model to M components, analyzing the crossover between O(3) and O(4) universality classes in frustrated antiferromagnets.

Findings

For physical spins, the critical behavior is O(4).

In commensurate cases, the behavior remains O(3).

A finite-temperature confinement-deconfinement transition is identified.

Abstract

We consider an anisotropic version of the $CP^{1}$ model which describes frustrated quantum antiferromagnets with incommensurate spin correlations. We extend the two-component spinon field, describing lattice spins, to the $M$-component complex vector, and show, in the $1/M$ expansion, that for arbitrary small incommensurability longitudinal and transverse stiffnesses tend to the same value as the system approaches the quantum critical point. For physical spins ($M=2$), this yields $O(4)$ critical behavior. However, if the spin structure is commensurate, the longitudinal stiffness is identically zero. In this case, the critical behavior is the same as in $O(3)$ sigma model. We show how the critical exponents interpolate between $O(3)$ and $O(4)$ values near the transition. We also show that the competition between these two fixed points leads to a confinement-deconfinement transition at a finite temperature.