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 ε 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 (ε,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 ε=0, driven by a spinodal point present above Tc, which induces strong metastability through Griffiths singularities effects and induces the absence of a two-step shape relaxation curve characteristic of glasses.