{"id":"openai-math/Logarithmic-Relative-Fluctuations-in-the-Weakly-Disordered-Planar-Ising-Model","pdf":"https://github.com/openai/math/blob/main/preprints/Logarithmic-Relative-Fluctuations-in-the-Weakly-Disordered-Planar-Ising-Model-October-5-2026/critical-relative-second-moment-weak-random-bond-ising.pdf","url":"https://github.com/openai/math/tree/main/preprints/Logarithmic-Relative-Fluctuations-in-the-Weakly-Disordered-Planar-Ising-Model-October-5-2026","tags":["statistical-mechanics","ising-model","disordered-systems","correlations"],"score":0,"title":"Logarithmic Relative Fluctuations in the Weakly Disordered Planar Ising Model","domain":"Probability and statistical mechanics","family":"218","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"Assuming the stated deterministic critical-reference estimates, we prove that the relative second moment of the quenched critical spin correlation in the square-lattice Ising model with independent fair bonds $`1\\pm\\varepsilon`$ grows as $`(\\log r)^{1/4+o(1)}`$ for each sufficiently small fixed ε > 0. The correlation is evaluated at the physical critical temperature, with the thermodynamic limit taken before the disorder moments and the large-distance limit.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Conformal universality for weakly interacting and random-bond Ising models"}