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On the Replica Symmetric Regime of the SK Model

With Christian Brennecke (Bonn)

On the Replica Symmetric Regime of the SK Model

In this talk I will review basic predictions for the high temperature regime, the so called replica symmetric regime, of the Sherrington-Kirkpatrick spin glass model. 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 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 A. Adhikari, A. Schertzer, P. von Soosten, C. Xu and H.-T. Yau.

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