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.
Energy landscape statistics of the random orthogonal model / Giardina', Cristian; M., Degli Esposti; S., Graffi. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - STAMPA. - 36:(2003), pp. 2983-2994. [10.1088/0305-4470/36/12/308]
Energy landscape statistics of the random orthogonal model
GIARDINA', Cristian;
2003
Abstract
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.
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