Probability and Mathematical Physics Seminar

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The de Almeida-Thouless line in the Sherrington-Kirkpatrick model

Speaker: Patrick Lopatto, University of North Carolina at Chapel Hill

Location: Warren Weaver Hall 1302

Date: Friday, October 16, 2026, 11 a.m.

Synopsis:

We show that in the Sherrington-Kirkpatrick model at inverse temperature beta with uniform external field h, replica symmetry holds for the set of pairs (beta, h) predicted by de Almeida and Thouless (1978). The proof proceeds by a direct analysis of the Parisi measure using the characterization provided by Jagannath and Tobasco (2017). This argument was found in the spring of 2026 with the assistance of large language models. If time permits, we will also discuss the landscape of rigorous spin glass theory in the wake of the OpenAI problem release.