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Finite-size mean bias of the Sherrington-Kirkpatrick free energy

P. M. Aronow, Patrick Lopatto

Palomar Registrypalomar/PALOMAR-2026-10-11-000006Oct 11, 2026math.PRscore 0

Formalization of a fixed-temperature N^(-7/10) bound for the finite-size mean bias of the zero-field Sherrington-Kirkpatrick model with independent standard Gaussian couplings and the unnormalized partition function. For every beta > 1, a positive constant depending on beta bounds the nonnegative pressure gap for every integer N >= 2. The selected results also establish the thermodynamic limit for beta > 0, the corresponding free-energy-density and expected log-partition corrections, a positive exponent saving over 2/3, and a full-sequence little-o improvement. The independently readable…

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