The Cavity Method at Zero Temperature

By M. M'ezard, Giorgio Parisi. 2002

336 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0782b6a96481129b0d04bc05c45ec25a53fbd07f

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

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Citations in the corpus

Statistical physics of inference: thresholds and algorithms (2015, methodology): “With the work of Mézard, Parisi and Zecchina on survey propagation [204], the statistical physics community learned that the replica and cavity calculations are as powerful when used as algorithms as they are when used as tools for analyzing the phase diagram.”
A survey of max-type recursive distributional equations (2004, methodology): “[62]) 1/X =d X∞ i=1 e−θξ iX i; S = R+ which is somewhat in the spirit of the linear case. 53 7.5 The cavity method The non-rigorouscavity method was developed in statistical physics in the 1980s: see [54] for a recent survey. Though typically applied to examples such as ground states of disordered I”
Edwards Statistical Mechanics for Jammed Granular Matter (2016, background): “7 in (Mézard and Parisi, 2003).”
MAX k-CUT and approximating the chromatic number of random graphs (2006, background): “For the physics reasoning that leads to this conjecture we refer the interested reader to [20, 24].”
Community detection in graphs (2009, background): “The minimum energy can be computed with the cavity method, or belief propagation, at zero temperature [405].”