Irreducible free energy expansion and overlaps locking in mean field spin glasses

Details Irreducible free energy expansion and overlaps locking in mean field spin glasses Irreducible free energy expansion and overlaps locking in mean field spin glasses

2006-07-26

arxiv.org/abs/cond-mat/0607688v1

Journal of Statistical Physics, Jan 2006, Pages 1 - 14

Physics

Condensed Matter

Disordered Systems and Neural Networks

19 pages

Scientific paper

10.1007/s10955-005-9006-6

We introduce a diagrammatic formulation for a cavity field expansion around the critical temperature. This approach allows us to obtain a theory for the overlap's fluctuations and, in particular, the linear part of the Ghirlanda-Guerra relationships (GG) (often called Aizenman-Contucci polynomials (AC)) in a very simple way. We show moreover how these constraints are "superimposed" by the symmetry of the model with respect to the restriction required by thermodynamic stability. Within this framework it is possible to expand the free energy in terms of these irreducible overlaps fluctuations and in a form that simply put in evidence how the complexity of the solution is related to the complexity of the entropy.

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