Extended variational principle for the Sherrington-Kirkpatrick spin-glass model

@article{Aizenman2003ExtendedVP,
  title={Extended variational principle for the Sherrington-Kirkpatrick spin-glass model},
  author={Michael Aizenman and Robert Sims and Shannon L. Starr},
  journal={Physical Review B},
  year={2003},
  volume={68},
  pages={214403}
}
The recent proof by Guerra that the Parisi ansatz provides a lower bound on the free energy of the Sherringtun-Kirkpatrick (SK) spin-glass model could have been taken as offering some support to the validity of the purported solution. In this work we present a broader variational principle, in which the lower bound as well as the actual value are expressed through an optimization procedure for which ultrametric/hierarchal structures form only a subset of the variational class. The validity of… 
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