The Complexity of Ising Spin Glasses
Disordered Systems and Neural Networks
2009-11-10 v2 Statistical Mechanics
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.
Keywords
Cite
@article{arxiv.cond-mat/0309113,
title = {The Complexity of Ising Spin Glasses},
author = {T. Aspelmeier and A. J. Bray and M. A. Moore},
journal= {arXiv preprint arXiv:cond-mat/0309113},
year = {2009}
}
Comments
Typos corrected