First-order phase transitions in spin-glass models with multiple paramagnetic solutions

The paramagnetic and the one-step replica-symmetry-breaking spin-glass solutions of a p-spin-glass model in the presence of a transverse field are studied in the neighborhood of the phase transition curve. Two qualitatively different regions are found in the phase diagram. For a transition temperature higher than a certain value Tc, the thermodynamic transition is of second order, otherwise it is of first order with latent heat. The temperature Tc is joined to a point in the phase diagram where a transition between two paramagnetic solutions happens. A discussion about the order of the thermodynamic-phase transition in the quantum random orthogonal model is presented