Phase coexistence and relaxation of the spherical frustrated Blume-Emery-Griffiths model with attractive particles coupling

We study the equilibrium and dynamical properties of a spherical version of the frustrated Blume-Emery-Griffiths model at mean-field level for attractive particle-particle coupling ($K>0$). Beyond a second-order transition line from a paramagnetic to a (replica symmetric) spin glass phase, the density-temperature phase diagram is characterized by a tricritical point from which, interestingly, a first-order transition line starts with coexistence of the two phases. In the Langevin dynamics the paramagnetic/spin glass discontinuous transition line is found to be dependent on the initial density; close to this line, on the paramagnetic side, the correlation-response plot displays interrupted aging