- 03-283 Michael Aizenman, Robert Sims, Shannon L. Starr
- An Extended Variational Principle for the SK Spin-Glass Model
(30K, 4 pages, RevTeX 4)
Jun 15, 03
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Abstract. The recent proof by F. Guerra that the Parisi ansatz provides a
lower bound on the free energy of the 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 ultrametic/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.