Thermodynamic Properties and Phase Transitions in a Mean-Field Ising Spin Glass on Lattice Gas: the Random Blume-Emery-Griffiths-Capel Model

The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable Replica Symmetric solution. When the temperature is decreased or the density increases, the system undergoes a phase transition to a Full Replica Symmetry Breaking spin-glass phase. The nature of the transition can be either of the second order (like in the Sherrington-Kirkpatrick model) or, at temperature below a given critical value, of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter and accompanied by a latent heat. In this last case coexistence of phases takes place. The thermodynamics is worked out in the Full Replica Symmetry Breaking scheme, and the relative Parisi equations are solved using a pseudo-spectral method down to zero temperature.