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Probability Seminars

The TAP-Plefka variational principle for mean field spin glasses

With David Belius (Basel)

The TAP-Plefka variational principle for mean field spin glasses

The Thouless-Anderson-Palmer (TAP) approach to the Sherrington-Kirckpatrick mean field spin glass model was described in one of the earliest papers on this model, but has subsequently been a complementary rather than the central component in the theory that has emerged in theoretical physics and mathematics. In this this talk I will recall the TAP approach, and describe how it can be reinterpreted as a variational principle in the spirit of the Gibbs variational principle. Furthermore I will present a rigorous proof of this TAP -Plefka variational principle in the case of the spherical Sherrington-Kirkpatrick model, which allows to compute the free energy based purely on a TAP analysis.

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