The Cavity Method at Zero Temperature

Journal of Statistical Physics - Tập 111 - Trang 1-34 - 2003
Marc Mézard1, Giorgio Parisi2
1Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris Sud, Orsay Cedex, France
2Dipartimento di Fisica, Sezione INFN, SMC and UdRm1 of INFM, Università di Roma “La Sapienza,”, Rome, Italy

Tóm tắt

In this note we explain the use of the cavity method directly at zero temperature, in the case of the spin glass on a lattice with a local tree like structure, which is the proper generalization of the usual Bethe lattice to frustrated problems. The computation is done explicitly in the formalism equivalent to “one step replica symmetry breaking;” we compute the energy of the global ground state, as well as the complexity of equilibrium states at a given energy. Full results are presented for a Bethe lattice with connectivity equal to three. The main assumptions underlying the one step cavity approach, namely the existence of many local ground states, are explicitely stated and discussed: some of the main obstacles towards a rigorous study of the problem with the cavity method are outlined.

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Journal of Statistical Physics

Tập 111

1-34

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