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

Details The massive $CP^{N-1}$ model for frustrated spin systems The massive $CP^{N-1}$ model for frustrated spin systems

1995-09-07

arxiv.org/abs/cond-mat/9509036v1

Nucl.Phys. B455 (1995) 648-684

Physics

Condensed Matter

55 pages, Latex

Scientific paper

10.1016/0550-3213(95)00514-S

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.

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