On the tail of the overlap probability distribution in the Sherrington-Kirkpatrick model

Abstract

We investigate the large deviation behaviour of the overlap probability density in the Sherrington-Kirkpatrick (SK) model using the coupled replica scheme, and we compare with the results of a large-scale numerical simulation. In the spin glass phase we show that, generically, for any model with continuous replica symmetry breaking (RSB), 1/N log PN(q) ≈ -A(|q| - qEA)3 and we compute the first correction to the expansion of A in powers of Tc - T for the SK model. We also study the paramagnetic phase, where results are obtained in the replica symmetric scheme that do not involve an expansion in powers of q - qEA or Tc - T. Finally we give precise semi-analytical estimates of P(|q| = 1). The overall agreement between the various points of view is very satisfactory.