Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2012-01-17
Physics
Condensed Matter
Disordered Systems and Neural Networks
Scientific paper
In these notes we review first in some detail the concept of random overlap structure (ROSt) applied to fully connected and diluted spin glasses. We then sketch how to write down the general term of the expansion of the energy part from the Boltzmann ROSt (for the Sherrington-Kirkpatrick model) and the corresponding term from the RaMOSt, which is the diluted extension suitable for the Viana-Bray model. From the ROSt energy term, a set of polynomial identities (often known as Aizenman-Contucci or AC relations) is shown to hold rigorously at every order because of a recursive structure of these polynomials that we prove. We show also, however, that this set is smaller than the full set of AC identities that is already known. Furthermore, when investigating the RaMOSt energy for the diluted counterpart, at higher orders, combinations of such AC identities appear, ultimately suggesting a crucial role for the entropy in generating these constraints in spin glasses.
Barra Adriano
Sollich Peter
No associations
LandOfFree
Notes on the polynomial identities in random overlap structures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Notes on the polynomial identities in random overlap structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Notes on the polynomial identities in random overlap structures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-97090