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We study the metastable states in Ising spin models with orthogonalinteraction matrices. We focus on three realizations of this model, the randomcase and two non-random cases, i.e.\ the fully-frustrated model on an infinitedimensional hypercube and the so-called sine-model. We use the mean-field (or{\sc tap}) equations which we derive by resuming the high-temperature expansionof the Gibbs free energy. In some special non-random cases, we can find theabsolute minimum of the free energy. For the random case we compute the averagenumber of solutions to the {\sc tap} equations. We find that theconfigurational entropy (or complexity) is extensive in the range$T_{\mbox{\tiny RSB}}<T<T_{\mbox{\tiny M}}$. Finally we present an apparentlyunrelated replica calculation which reproduces the analytical expression forthe total number of {\sc tap} solutions.

Mean-field equations for spin models with orthogonal interaction matrices