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

The recent proof by Guerra that the Parisi ansatz provides a lower bound on the free energy of the Sherrington-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 Parisi’s ansatz for the SK model is still in question. The new variational principle may be of help in critical review of the issue.