  We develop a simple method to study the high temperature, or high external
field, behavior of the Sherrington-Kirkpatrick mean field spin glass model. The
basic idea is to couple two different replicas with a quadratic term, trying to
push out the two replica overlap from its replica symmetric value. In the case
of zero external field, our results reproduce the well known validity of the
annealed approximation, up to the known critical value for the temperature. In
the case of nontrivial external field, we prove the validity of the
Sherrington-Kirkpatrick replica symmetric solution up to a line, which falls
short of the Almeida-Thouless line, associated to the onset of the spontaneous
replica symmetry breaking, in the Parisi Ansatz. The main difference with the
method, recently developed by Michel Talagrand, is that we employ a quadratic
coupling, and not a linear one. The resulting flow equations, with respect to
the 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 and
overlap fluctuations, in the region where replica symmetry has been shown to
hold.
