  We study spin glasses on random lattices with finite connectivity. In the
infinite connectivity limit they reduce to the Sherrington Kirkpatrick model.
In this paper we investigate the expansion around the high connectivity limit.
Within the replica symmetry breaking scheme at two steps, we compute the free
energy at the first order in the expansion in inverse powers of the average
connectivity (z), both for the fixed connectivity and for the fluctuating
connectivity random lattices. It is well known that the coefficient of the 1/z
correction for the free energy is divergent at low temperatures if computed in
the one step approximation. We find that this annoying divergence becomes much
smaller if computed in the framework of the more accurate two steps breaking.
Comparing the temperature dependance of the coefficients of this divergence in
the replica symmetric, one step and two steps replica symmetry breaking, we
conclude that this divergence is an artefact due to the use of a finite number
of steps of replica symmetry breaking. The 1/z expansion is well defined also
in the zero temperature limit.
