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We apply for the first time a new one-loop topological expansion around theBethe solution to the spin-glass model with field in the high connectivitylimit, following the methodological scheme proposed in a recent work. Theresults are completely equivalent to the well known ones, found by standardfield theoretical expansion around the fully connected model (Bray and Roberts1980, and following works). However this method has the advantage that thestarting point is the original Hamiltonian of the model, with no need to definean associated field theory, nor to know the initial values of the couplings,and the computations have a clear and simple physical meaning. Moreover thisnew method can also be applied in the case of zero temperature, when the Bethemodel has a transition in field, contrary to the fully connected model that isalways in the spin glass phase. Sharing with finite dimensional model thefinite connectivity properties, the Bethe lattice is clearly a better startingpoint for an expansion with respect to the fully connected model. The presentwork is a first step towards the generalization of this new expansion to moredifficult and interesting cases as the zero-temperature limit, where theexpansion could lead to different results with respect to the standard one.

One-loop topological expansion for spin glasses in the large connectivity limit