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We develop a simple method to study the high temperature, or high externalfield, behavior of the Sherrington-Kirkpatrick mean field spin glass model. Thebasic idea is to couple two different replicas with a quadratic term, trying topush out the two replica overlap from its replica symmetric value. In the caseof zero external field, our results reproduce the well known validity of theannealed approximation, up to the known critical value for the temperature. Inthe case of nontrivial external field, we prove the validity of theSherrington-Kirkpatrick replica symmetric solution up to a line, which fallsshort of the Almeida-Thouless line, associated to the onset of the spontaneousreplica symmetry breaking, in the Parisi Ansatz. The main difference with themethod, recently developed by Michel Talagrand, is that we employ a quadraticcoupling, and not a linear one. The resulting flow equations, with respect tothe parameters of the model, turn out to be much simpler, and more tractable.By applying the cavity method, we show also how to determine free energy andoverlap fluctuations, in the region where replica symmetry has been shown tohold.Comment: 17 pages; added references; corrected typo

Quadratic replica coupling in the Sherrington–Kirkpatrick mean field spin glass model