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Quenched computation of the dependence of complexity on the free energy in the Sherrington-Kirkpatrick model

A. Crisanti, L. Leuzzi, G. Parisi, T. Rizzo
2004 Physical Review B  

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2003 pre-print
arXiv:cond-mat/0309256v1 fatcat:pk5gqa5qtza45o2sybiazbswlq
2004 accepted
arXiv:cond-mat/0309256v3 fatcat:hkqbgpjzivcy7c4wn4glngzkim
2003 pre-print
arXiv:cond-mat/0309256v2 fatcat:c3l6wlizkfhd3dsz2e6nqu2sqe
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
more » ... 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.
doi:10.1103/physrevb.70.064423 fatcat:xlpxra745fbw7njcioqlufwhuy
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A. Crisanti, L. Leuzzi, G. Parisi, T. Rizzo. "Quenched computation of the dependence of complexity on the free energy in the Sherrington-Kirkpatrick model." Physical Review B 70.6 (2004)