The massive $C{P}^{N-1}$ model for frustrated spin systems

Abstract

We study the classical $SU(N)\otimes U(1)/SU(N-1)\otimes U(1)$ Non Linear Sigma model which is the continuous low energy effective field theory for $N$ component frustrated spin systems. The $\beta$ functions for the two coupling constants of this model are calculated around two dimensions at two loop order in a low temperature expansion. Our study is completed by a large $N$ analysis of the model. The $\beta$ functions for the coupling constants and the mass gap are calculated in all dimensions between 2 and 4 at order $1/N$. As a main result we show that the standard procedure at the basis of the $1/N$ expansion leads to results that partially contradict those of the weak coupling analysis. We finally present the procedure that reconciles the weak coupling and large $N$ analysis, giving a consistent picture of the expected scaling of frustrated magnets.

55 pages, Latex

References in corpus (3)

• Universal Magnetic Properties of Frustrated Quantum Antiferromagnets in Two Dimensions
• Quantum Phase Transition in Frustrated Two-Dimensional Antiferromagnets
• A Renormalization Group Study of Helimagnets in D=2+EPSILON Dimensions

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