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The Spectra of Local Minima in Spin-Glass Models

The spectra of spin models have been investigated in computation experiments. For the Sherrington-Kirkpatrick and Edwards-Anderson models we have determined the basic spectral characteristics: the average depth of a local minimum, the spectrum width, the depth of the global minimum. The experimental data are used to build the relations between these quantities and the model dimensionality N and find their asymptotic values for N goes to infinity.