Journal of Statistical Physics

, Volume 123, Issue 3, pp 601-614

First online:

Irreducible Free Energy Expansion and Overlaps Locking in Mean Field Spin Glasses

  • Adriano BarraAffiliated withDepartment of Mathematics, King's College LondonDipartimento di Fisica, Universita' di Roma “La Sapienza,” Email author 

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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.

Key Words

Cavity field Ghirlanda–Guerra stochastic stability Aizenman-Contucci polynomials