Irreducible Free Energy Expansion and Overlaps Locking in Mean Field Spin Glasses
- Adriano Barra
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Following the works of Guerra, 1995; Aizenmar and Contucci, J. State. Phys. 92 (5–6): 765–783 (1998), 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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- Irreducible Free Energy Expansion and Overlaps Locking in Mean Field Spin Glasses
Journal of Statistical Physics
Volume 123, Issue 3 , pp 601-614
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- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
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- Cavity field
- stochastic stability
- Aizenman-Contucci polynomials
- Industry Sectors
- Adriano Barra (1) (2)
- Author Affiliations
- 1. Department of Mathematics, King's College London, Strand, WC2R 2LS, London, UK
- 2. Dipartimento di Fisica, Universita' di Roma “La Sapienza,”, P.le Aldo Moro 2, 00185, Roma, Italy