We compute the complexity [logarithm of the number of Thouless-Anderson-Palmer (TAP) states] associated with minima and index-one saddle points of the TAP free energy. Higher-index saddles have smaller complexities. The two leading complexities are equal, consistent with the Morse theorem on the total number of turning points, and have the value given by Bray and Moore [J. Phys. C, ()]]. In the thermodynamic limit, TAP states of all free energies become marginally stable.
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Aspelmeier et al. (2004) studied this question.
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