  We study the thermodynamics and the properties of the stationary points
(saddles and minima) of the potential energy for a phi^4 mean field model. We
compare the critical energy Vc (i.e. the potential energy V(T) evaluated at the
phase transition temperature Tc) with the energy V{theta} at which the saddle
energy distribution show a discontinuity in its derivative. We find that, in
this model, Vc >> V{theta}, at variance to what has been found in the
literature for different mean field and short ranged systems. By direct
calculation of the energy Vs(T) of the ``inherent saddles'', i.e. the saddles
visited by the equilibrated system at temperature T, we find that Vs(Tc) ~
V{theta}. Thus, we argue that the thermodynamic phase transition is related to
a change in the properties of the inherent saddles rather then to a change of
the topology of the potential energy surface at T=Tc. Finally, we discuss the
approximation involved in our analysis and the generality of our method.
