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Replica symmetry up to the de Almeida–Thouless line in the Sherrington–Kirkpatrick model

P. M. Aronow, Patrick Lopatto

Palomar Registrypalomar/PALOMAR-2026-10-09-000013Oct 9, 2026math.PRscore 0

A Lean formalization of the positive-field Sherrington–Kirkpatrick results in Patrick Lopatto's arXiv:2604.11921v2. The selected registry claims are convergence of the expected finite-volume free energy to the concrete replica-symmetric Gaussian formula for beta > 0, h > 0, and AT parameter at most one, including equality; and an exact description of the positive-field AT boundary as a positive strictly increasing smooth graph on beta > 1, tending to zero at beta = 1 from the right, together with (1,0). The repository also contains the numbered PDE, stochastic-process, moment, and…

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