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

Abstract

The space of solutions of the exact renormalization group fixed point equations of the two-dimensional $R{P}^{N-1}$ model, which we recently obtained within the scale invariant scattering framework, is explored for continuous values of $N\ge 0$. 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 $N^{\ast }=\mathrm{2.24421..}$, 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 $N$.

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