论文信息 - Metastable configurations on the Bethe lattice.

Metastable configurations on the Bethe lattice.

We present a general analytic method to compute the number of metastable configurations as a function of the energy for a system of interacting Ising spins on the Bethe lattice. Our approach is based on the cavity method. We apply it to the case of ferromagnetic interactions, and also to the binary and Gaussian spin glasses. Most of our results are obtained within the replica symmetric ansatz, but we illustrate how replica symmetry breaking can be performed.

A Pagnani | G Parisi | M Ratiéville

[1] M. Mézard,et al. Mean-field theory of randomly frustrated systems with finite connectivity , 1987 .

[2] M. Mézard,et al. The Cavity Method at Zero Temperature , 2002, cond-mat/0207121.

[3] Kanter,et al. Mean-field theory of spin-glasses with finite coordination number. , 1987, Physical review letters.

[4] Metastable configurations of spin models on random graphs. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5] M. Mézard,et al. Random K-satisfiability problem: from an analytic solution to an efficient algorithm. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6] D. S. Dean. Metastable states of spin glasses on random thin graphs , 2000 .

[7] Remi Monasson,et al. From inherent structures to pure states: Some simple remarks and examples , 1999 .

[8] P. Mottishaw,et al. On the stability of randomly frustrated systems with finite connectivity , 1987 .

[9] Metastable states of a ferromagnet on random thin graphs , 2000, cond-mat/0011265.

[10] M. Mézard,et al. The Bethe lattice spin glass revisited , 2000, cond-mat/0009418.

[11] M. Mézard,et al. Spin Glass Theory and Beyond , 1987 .

[12] D. Aldous. Asymptotics in the random assignment problem , 1992 .

[13] Tapping thermodynamics of the one-dimensional Ising model , 2001, cond-mat/0102204.