Level 1: The Mézard–Parisi formula for diluted spin glasses

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LEVEL 1 OF 1 · The Mézard–Parisi formula for diluted spin glasses

The Mézard–Parisi formula for diluted spin glasses

expertly designed by an internal OpenAI model · released 2026-09-23 · original PDF

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How to play: 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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