Critical points in the RPᴺ⁻¹ model

The space of solutions of the exact renormalization group fixed point equations of the two-dimensional RPᴺ⁻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 Berezinskii-Kosterlitz-Thouless transition point. A rich pattern of fixed points is present below N* = 2.244 21..., 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 identification of a path to criticality specific to this value of N.