All-temperature pressure of orthogonally invariant Ising spin glasses
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
Gives an exact variational formula for the limiting pressure of orthogonally invariant Ising spin glasses at every fixed temperature, both almost surely and in expectation. The coupling matrix is a Haar-random rotation of a deterministic spectrum converging to a compactly supported law, with extreme eigenvalues converging to its support edges. The zero-field ground-state energy follows as temperature tends to zero.
Read the manuscripts
Short excerpts below come from OpenAI's abstracts. The full abstract and original PDF preserve the paper's precise scope.
MANUSCRIPT 01
All-temperature pressure for orthogonally invariant Ising spin glasses
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…
Full source abstract
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.
This exact PDF is not listed in the imported formalization catalogue. Family scope notes may contain further information.
New mathematical reasoning could help AI tackle harder scientific and computational problems. How reliably these skills transfer beyond mathematics will determine how much they contribute to general intelligence.