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 ⩾ 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.

我们最近在尺度不变散射框架内获得了二维RP ^{N -1}模型的精确重整化群不动点方程的解空间，探索了N ⩾ 0 的连续值。仅在N = 2时发生，并且允许多条不动点线在别列津斯基-科斯特利茨-Thouless 过渡点相交。在N * = 2.244 21‥以下存在丰富的固定点模式，而在O ( N ( N + 1)/2 − 1) 普遍性类别中只有零温度临界性可以出现在该值以上。N处额外解的解释 = 3 需要识别特定于该N值的关键性路径。