{"id":"palomar/PALOMAR-2026-10-23-000010","url":"https://github.com/masakioshikawa/rp2-rp3-lean/tree/ab120db3ae50756b2f640400aeca757a0ff9dbb5","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-23-000010-v1.json","repo":"https://github.com/masakioshikawa/rp2-rp3-lean","tags":["math-ph","cond-mat.stat-mech","msc:82B20","msc:82B26","statistical-mechanics","lattice-models","correlation-decay"],"score":0,"title":"Log-square quadrupolar correlation decay in two-dimensional RP2 and RP3 models","trust":"high","domain":"math-ph","source":"palomar","authors":["Masaki Oshikawa"],"reviews":0,"subject":"math-ph","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-23","reactions":{},"formalized":true,"formalizes":[{"title":"Faster-than-power-law decay of order parameter correlations in the two-dimensional RP2 model: a rigorous result by vibe-proving","identifier":"https://doi.org/10.5281/zenodo.23549037","relationship":"formalizes"},{"title":"Exponential decay in two-dimensional classical O(n) models","identifier":"https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a","relationship":"adapts"}]}