Random Matrices and Complexity of Spin Glasses

@article{Auffinger2010RandomMA,
  title={Random Matrices and Complexity of Spin Glasses},
  author={Antonio Auffinger and G{\'e}rard Ben Arous and Jiř{\'i} {\vC}ern{\'y}},
  journal={Communications on Pure and Applied Mathematics},
  year={2010},
  volume={66}
}
We give an asymptotic evaluation of the complexity of spherical p‐spin spin glass models via random matrix theory. This study enables us to obtain detailed information about the bottom of the energy landscape, including the absolute minimum (the ground state), and the other local minima, and describe an interesting layered structure of the low critical values for the Hamiltonians of these models. We also show that our approach allows us to compute the related TAPcomplexity and extend the… 
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