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

Abstract

The space of solutions of the exact renormalization group fixed point equations of the twodimensional RP N −1 model, which we recently obtained within the scale invariant scattering framework, is explored for continuous values of N ≥ 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 .