Ising M-p-spin mean-field model for the structural glass: Continuous versus discontinuous transition

The critical behavior of a family of fully connected mean-field models with quenched disorder, the M-p Ising spin glass, is analyzed, displaying a crossover between a continuous and a random first order phase transition as a control parameter is tuned. Due to its microscopic properties the model is straightforwardly extendable to finite dimensions in any geometry.