Faster-than-power-law decay of order parameter correlations in the two-dimensional RP2 model: a rigorous result by vibe-proving
We consider the $RP^2$ model on the two-dimensional square lattice with nearest-neighbor interactions. It is obtained by replacing the spin in the standard classical Heisenberg model with a director, which does not distinguish two opposite directions. Unlike the standard classical Heisenberg model or the O(3) nonlinear sigma model, the $RP^2$ (and its cousin $RP^3$) model allows point vortex defects classified by $\pi_1(RP^2)=Z_2$ in two dimensions. It is tempting to expect the $Z_2$ vortices to induce a phase transition analogous to the well-established Berezinskii-Kosterlitz-Thouless…
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