The Complexity of Ising Spin Glasses

Details The Complexity of Ising Spin Glasses The Complexity of Ising Spin Glasses

2003-09-04

arxiv.org/abs/cond-mat/0309113v2

Phys. Rev. Lett. 92, 087203 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Typos corrected

Scientific paper

10.1103/PhysRevLett.92.087203

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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