Quenched Computation of the Complexity of the Sherrington-Kirkpatrick Model

Details Quenched Computation of the Complexity of the Sherrington-Kirkpatrick Model Quenched Computation of the Complexity of the Sherrington-Kirkpatrick Model

2003-09-10

arxiv.org/abs/cond-mat/0309256v3

Phys. Rev. B 70, 064423 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

19 pages, 13 figures. Some formulas added corrected, changes in discussion and conclusion, one figure added

Scientific paper

10.1103/PhysRevB.70.064423

The quenched computation of the complexity in the Sherrington-Kirkpatrick model is presented. A modified Full Replica Symmetry Breaking Ansatz is introduced in order to study the complexity dependence on the free energy. Such an Ansatz corresponds to require Becchi-Rouet-Stora-Tyutin supersymmetry. The complexity computed this way is the Legendre transform of the free energy averaged over the quenched disorder. The stability analysis shows that this complexity is inconsistent at any free energy level but the equilibirum one. The further problem of building a physically well defined solution not invariant under supersymmetry and predicting an extensive number of metastable states is also discussed.

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