  We investigate the critical behavior of a three-dimensional short-range spin
glass model in the presence of an external field $\eps$ conjugated to the
Edwards-Anderson order parameter. In the mean-field approximation this model is
described by the Adam-Gibbs-DiMarzio approach for the glass transition. By
Monte Carlo numerical simulations we find indications for the existence of a
line of critical points in the plane $(\eps,T)$ which separates two
paramagnetic phases and terminates in a critical endpoint. This line of
critical points appears due to the large degeneracy of metastable states
present in the system (configurational entropy) and is reminiscent of the
first-order phase transition present in the mean-field limit. We propose a
scenario for the spin-glass transition at $\eps=0$, driven by a spinodal point
present above $T_c$, which induces strong metastability through Griffiths
singularities effects and induces the absence of a two-step shape relaxation
curve characteristic of glasses.
