The massive CPN−1 model for frustrated spin systems Original Research Article

We study the classical SU(N) ⋇ U(1)/SU(N − 1) ⋇ U(1) non-linear sigma model which is the continuous low-energy effective field theory for N-component frustrated spin systems. The β 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 β 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.