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

TL;DR

This paper analyzes a classical nonlinear sigma model relevant for frustrated spin systems, calculating beta functions and mass gaps across dimensions, and reconciling large N and weak coupling approaches for a consistent physical picture.

Contribution

It provides a comprehensive two-loop and large N analysis of the model, clarifying discrepancies between different theoretical approaches.

Findings

Beta functions calculated at two loops in two dimensions.

Mass gap computed across dimensions between 2 and 4.

Reconciliation of large N and weak coupling results for frustrated magnets.

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.