Complexity and line of critical points in a short-range spin-glass model

We investigate the critical behavior of a three-dimensional short-range spin-glass model in the presence of an external field epsilon 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 (epsilon, T) which separates two paramagnetic phases, Although we may not exclude the possibility that this line is a crossover behavior, its presence is direct consequence of the large degeneracy of metastable states present in the system and its character reminiscent of the first-order phase transition present in the mean-field limit, We propose a scenario for the spin-glass transition at epsilon = 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. (C) 2000 Elsevier Science B.V. Ail rights reserved.