Log-square quadrupolar correlation decay in two-dimensional RP2 and RP3 models
For the two-dimensional nearest-neighbor RP2 and RP3 director models, the absolute quadrupolar two-point correlation is bounded by C exp(-c (log(2+r))^2) at every finite bound on the dimensionless coupling. The positive constants are uniform over finite square-lattice subgraphs, arbitrary signed edge couplings within that bound, and observation sites; r is the integer lattice infinity distance. The compared statements use explicit normalized spherical product measures and Gibbs-integral quotients, with observable (n_x dot n_y)^2 - 1/3 or - 1/4, respectively. No response estimate or decay…
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