Metastable states in the Blume-Emery-Griffiths spin-glass model

We study the Blume-Emery-Griffiths spin-glass model in the presence of an attractive coupling between real replicas, and evaluate the effective potential as a function of the density overlap. We find that there is a region, above the first-order transition of the model, where metastable states with a large density overlap exist. The line where these metastable states appear should correspond to a purely dynamical transition, with a breaking of ergodicity. Differently from what happens in p-spin glasses, in this model the dynamical transition would not be the precursor of a one-step replica symmetry breaking transition, but (probably) of a full replica symmetry breaking transition.