Critical points in the $CP^{N-1}$ model

TL;DR

This paper employs scale invariant scattering theory to precisely identify the renormalization group fixed points of the two-dimensional $CP^{N-1}$ model, revealing special degeneracies and new critical points for different values of N.

Contribution

It provides exact equations for fixed points of the 2D $CP^{N-1}$ model and uncovers new branches of fixed points for N<2 related to intersecting loop gases.

Findings

Fixed points for N≥2 match the $O(N^2-1)$ model due to degeneracies.

Special degeneracies at N=2 and 3 reduce the solution space.

New fixed point branches emerge for N<2, relevant for loop gas criticality.

Abstract

We use scale invariant scattering theory to obtain the exact equations determining the renormalization group fixed points of the two-dimensional $CP^{N-1}$ model, for $N$ real. Also due to special degeneracies at $N=2$ and 3, the space of solutions for $N\geq 2$ reduces to that of the $O(N^2-1)$ model, and accounts for a zero temperature critical point. For $N<2$ the space of solutions becomes larger than that of the $O(N^2-1)$ model, with the appearance of new branches of fixed points relevant for criticality in gases of intersecting loops.