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

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

1996-02-14

arxiv.org/abs/cond-mat/9602077v1

Phys.Rev. B53 (1996) 14729

Physics

Condensed Matter

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Scientific paper

10.1103/PhysRevB.53.R14729

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.

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