Multispin Ising spin glasses with ferromagnetic interactions

We consider the thermodynamics of an infinite-range Ising p-spin glass model with an additional r-spin ferromagnetic interaction. For r = 2 there is a continuous transition to a ferromagnetic phase, while for r > 2 the transition is first order. We find both glassy and non-glassy ferromagnetic phases, with replica symmetry breaking of both the one step and full varieties. We obtain new results for the case where r = p > 2, demonstrating the existence of a non-glassy ferromagnetic phase, of significance to error-correcting codes.