OpenAI research collection · 1 manuscript · Source checked 2026-10-19
The idea in plain language
A spin glass is a mathematical model with competing, disordered interactions. This manuscript claims a proof of a formula for the limiting free energy of a specified class of diluted models, under explicit assumptions on their interactions.
Why it matters
Such models connect probability, physics and optimisation. The proof's scope is a defined class of systems, not every disordered material.
Read the technical source claim
Proves the Mézard–Parisi hierarchical cavity formula for Poisson-diluted even-arity Ising models satisfying the Panchenko–Talagrand factorization and positivity assumptions, with only first-moment integrability. The limiting free energy equals the infimum over finite-depth hierarchical trial laws. This includes the Viana–Bray model, symmetric diluted even-spin models, and weighted soft even-K satisfiability.
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
The Mézard–Parisi formula for diluted spin glasses
We prove the Mézard–Parisi hierarchical cavity formula for diluted even-arity Ising models in the Panchenko–Talagrand class. This resolves the variational equality conjecture for that class: the limiting pressure equals the infimum of the trial functional over all finite hierarchy depths and trial laws. Only first moments of…
Full source abstract
We prove the Mézard–Parisi hierarchical cavity formula for diluted even-arity Ising models in the Panchenko–Talagrand class. This resolves the variational equality conjecture for that class: the limiting pressure equals the infimum of the trial functional over all finite hierarchy depths and trial laws. Only first moments of the interaction and external field are required.
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