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

TL;DR

This paper explores the fixed point solutions of the two-dimensional $RP^{N-1}$ model across different N values, revealing unique critical behaviors and phase transitions, including the BKT transition at N=2.

Contribution

It provides a detailed analysis of the solution space of the $RP^{N-1}$ model's renormalization group equations for continuous N, uncovering new fixed point structures and critical phenomena.

Findings

Quasi-long-range order only at N=2

Multiple fixed points meet at the BKT transition

Criticality patterns change at N*≈2.24421

Abstract

The space of solutions of the exact renormalization group fixed point equations of the two-dimensional $RP^{N-1}$ model, which we recently obtained within the scale invariant scattering framework, is explored for continuous values of $N\geq 0$. Quasi-long-range order occurs only for $N=2$, and allows for several lines of fixed points meeting at the BKT transition point. A rich pattern of fixed points is present below $N^*=2.24421..$, while only zero temperature criticality in the $O(N(N+1)/2-1)$ universality class can occur above this value. The interpretation of an extra solution at $N=3$ requires the identitication of a path to criticality specific to this value of $N$.