{"id":"openai-math/All-temperature-pressure-for-orthogonally-invariant-Ising-spin-glasses","pdf":"https://github.com/openai/math/blob/main/preprints/All-temperature-pressure-for-orthogonally-invariant-Ising-spin-glasses-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/All-temperature-pressure-for-orthogonally-invariant-Ising-spin-glasses-September-25-2026","tags":["probability","spin-glasses","random-matrices"],"score":0,"title":"All-temperature pressure for orthogonally invariant Ising spin glasses","domain":"Probability and statistical mechanics","family":"234","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We determine the limiting pressure of an Ising spin glass with Haar orthogonal eigenvectors, a compact limiting spectral law, and no asymptotic outliers, at every fixed temperature. The pressure converges in expectation and almost surely to a variational formula. We also give the limiting pressure with deterministic external fields whose empirical laws converge in first-moment transport distance, and derive a formula for the zero-field ground-state energy by taking temperature to zero.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"All-temperature pressure of orthogonally invariant Ising spin glasses"}