Energy landscape statistics of the random orthogonal model

The random orthogonal model (ROM) of Marinari-Parisi-Ritort [13, 14] is a model of statistical mechanics where the couplings among the spins are defined by a matrix chosen randomly within the orthogonal ensemble.. It reproduces the most relevant properties of the Parisi solution of the Sherrington-Kirkpatrick model. Here we compute the energy distribution, and work out an estimate for the two-point correlation function. Moreover, we show an exponential increase with the system size of the number of metastable states also for non-zero magnetic field.