On the $RP^{N-1}$ and $CP^{N-1}$ universality classes

TL;DR

This paper explores the universality classes of 2D $RP^{N-1}$ and $CP^{N-1}$ models, providing exact fixed point equations and analyzing subtle differences in solutions related to interaction types.

Contribution

It presents the exact fixed point equations and solution spaces for these models, clarifying subtleties linked to ferromagnetic and antiferromagnetic interactions.

Findings

Derived exact fixed point equations for $RP^{N-1}$ and $CP^{N-1}$ models

Identified subtleties in solutions related to interaction types

Clarified differences between ferromagnetic and antiferromagnetic cases

Abstract

We recently determined the exact fixed point equations and the spaces of solutions of the two-dimensional $RP^{N-1}$ and $CP^{N-1}$ models using scale invariant scattering theory. Here we discuss subtleties hidden in some solutions and related to the difference between ferromagnetic and antiferromagnetic interaction.