Probability and Mathematical Physics Seminar

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Existence of Full Replica Symmetry Breaking for the Sherrington-Kirkpatrick Model

Speaker: Yuxin Zhou, University of Chicago

Location: Warren Weaver Hall 1302

Date: Friday, September 26, 2025, 11:10 a.m.

Synopsis:

The Sherrington–Kirkpatrick (SK) model is a well-known model for spin glasses that originated in physics. In a series of ground-breaking articles by Giorgio Parisi proposed in 1979, it was predicted that the limiting free energy of the SK model is given by a variational principle, known as the Parisi formula, and its minimizer, known as the Parisi measure, will be full replica symmetry breaking (FRSB) at low temperature. The former one was confirmed in the past decade. However the existence of FRSB has not been established before. In this talk, I will show that the Parisi measure of the SK model is FRSB slightly beyond the high temperature. I will also talk about the structure of the corresponding Parisi measure.