  We apply for the first time a new one-loop topological expansion around the
Bethe solution to the spin-glass model with field in the high connectivity
limit, following the methodological scheme proposed in a recent work. The
results are completely equivalent to the well known ones, found by standard
field theoretical expansion around the fully connected model (Bray and Roberts
1980, and following works). However this method has the advantage that the
starting point is the original Hamiltonian of the model, with no need to define
an associated field theory, nor to know the initial values of the couplings,
and the computations have a clear and simple physical meaning. Moreover this
new method can also be applied in the case of zero temperature, when the Bethe
model has a transition in field, contrary to the fully connected model that is
always in the spin glass phase. Sharing with finite dimensional model the
finite connectivity properties, the Bethe lattice is clearly a better starting
point for an expansion with respect to the fully connected model. The present
work is a first step towards the generalization of this new expansion to more
difficult and interesting cases as the zero-temperature limit, where the
expansion could lead to different results with respect to the standard one.
