Continuous and discontinuous transitions in generalized p-spin glass models

We investigate the generalized p-spin models that contain arbitrary diagonal operators \hat{U} with no reflection symmetry. We derive general equations that give an opportunity to uncover the behavior of the system near the glass transition at different (continuous) p. The quadrupole glass with J = 1 is considered as an illustrative example. It is shown that the crossover from continuous to discontinuous glass transition to the one-step replica breaking solution (1RSB) takes place at p = 3.3 for this model. For p < 2 + Δp, where Δp = 0.5 is a finite value, the stable 1RSB solution disappears. This behavior is very different from that of the p-spin Ising glass model.