  In previous work, we have developed a simple method to study the behavior of
the Sherrington-Kirkpatrick mean field spin glass model for high temperatures,
or equivalently for high external fields. The basic idea was 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 reproduced the well known validity of the annealed approximation,
up to the known critical value for the temperature. In the case of nontrivial
external field, our method could prove the validity of the
Sherrington-Kirkpatrick replica symmetric solution up to a line, which fell
short of the Almeida-Thouless line, associated to the onset of the spontaneous
replica symmetry breaking, in the Parisi Ansatz. Here, we make a strategic
improvement of the method, by modifying the flow equations, with respect to the
parameters of the model. We exploit also previous results on the overlap
fluctuations in the replica symmetric region. As a result, we give a simple
proof that replica symmetry holds up to the critical Almeida-Thouless line, as
expected on physical grounds. Our results are compared with the
characterization of the replica symmetry breaking line previously given by
Talagrand. We outline also a possible extension of our methods to the broken
replica symmetry region.
