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The Complexity of Ising Spin Glasses

T. Aspelmeier·A. J. Bray·M. A. Moore
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Abstract

We compute the complexity (logarithm of the number of 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 in [A. J. Bray and M. A. Moore, J. Phys. C 13, L469 (1980)]. In the thermodynamic limit, TAP states of all free energies become marginally stable.

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T. Aspelmeier, A. J. Bray, M. A. Moore. 2003-09-30. The Complexity of Ising Spin Glasses. https://doi.org/10.1103/physrevlett.92.087203

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