Many-body spin glasses in the microcanonical ensemble

We investigate the p-spin model with Gaussian-distributed random interactions in the microcanonical ensemble using the replica theory. For p = 2, there are only second-order phase transitions and we recover the results of Sherrington and Kirkpatrick obtained in the canonical ensemble. For p >= 3, the transition between the ferromagnetic and paramagnetic phases is of first order, and the microcanonical and canonical ensembles give different results. We also discuss the ensemble inequivalence of the random energy model, corresponding to the limit p -> infinity. This is the first systematic treatment of spin glasses with long-range interactions in the microcanonical ensemble, which shows how the two ensembles give different results.