Operator Norm Bounds on the Correlation Matrix of the SK Model

Abstract: In this talk I will review basic predictions for the high temperature regime, the so called replica symmetric regime, of the Sherrington-Kirkpatrick mean field spin glass. I will recall the TAP equations, their derivation and their validity in connection with the decay of the two point correlation functions. For the simplified case of vanishing external field, I will present some details on recent results that characterize the susceptibility of the model as a resolvent of the interaction matrix, which predicts in a simple way the (well-known) RS-RSB transition temperature. The talk is based on joint work with Adrien Schertzer, Changji Xu and Horng-Tzer Yau.

mathematical physicsspectral theory

Audience: researchers in the topic

Munich-Copenhagen-Santiago Mathematical Physics seminar

Series comments: The MAS-MP seminar series has now changed name to MCS-MP.

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