Journal of Statistical Physics

, Volume 147, Issue 2, pp 351–374 | Cite as

Notes on the Polynomial Identities in Random Overlap Structures

Article
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Abstract

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.

Keywords

Polynomial Identity Permutation Symmetry Integer Partition Replica Trick Summation Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgements

The authors are grateful to Francesco Guerra for useful conversations.

AB acknowledges the FIRB grant RBFR08EKEV.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsKing’s College LondonLondonUK
  2. 2.Dipartimento di FisicaSapienza Università di RomaRomeItaly

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