Exponential control of overlap in the replica method for p-spin Sherrington-Kirkpatrick model

Details Exponential control of overlap in the replica method for p-spin Sherrington-Kirkpatrick model Exponential control of overlap in the replica method for p-spin Sherrington-Kirkpatrick model

2007-01-30

arxiv.org/abs/math-ph/0701074v1

Journal of Statistical Physics, 2008, Vol. 130, No. 5, 831-842.

Physics

Mathematical Physics

Scientific paper

10.1007/s10955-007-9463-1

Recently, Michel Talagrand computed the large deviations limit $\lim_{N\to\infty}(Na)^{-1}\log \e Z_N^a$ for the moments of the partition function $Z_N$ in the Sherrington-Kirkpatrick model for all real $a\geq 0.$ For $a\geq 1$ the limit is given by Guerra's inverse bound and this result extends the classical physicist's replica method that corresponds to integer $a.$ We give a new proof for $a\geq 1$ in the case of the pure $p$-spin SK model that provides a strong exponential control of the overlap.

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