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Metastable configurations on the Bethe lattice.

A Pagnani1, G Parisi, M Ratiéville

  • 1Dipartimento di Fisica, SMC, INFM, Università degli Studi di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185 Rome, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
Summary

We developed a new analytic method using the cavity method to count metastable states in interacting Ising spin systems. This approach is applicable to ferromagnetic and spin glass models on the Bethe lattice.

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Area of Science:

  • Statistical mechanics
  • Computational physics
  • Condensed matter theory

Background:

  • Understanding the complex behavior of magnetic systems requires characterizing their metastable states.
  • The Bethe lattice provides a simplified yet insightful model for studying interacting spin systems.

Purpose of the Study:

  • To introduce a general analytic method for calculating the number of metastable configurations.
  • To apply this method to ferromagnetic and spin glass models on the Bethe lattice.

Main Methods:

  • The study employs the cavity method, a powerful technique in statistical physics.
  • The replica symmetric ansatz is used for most calculations.
  • Replica symmetry breaking is demonstrated as an extension.

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Main Results:

  • A general analytic method is presented for computing metastable configurations as a function of energy.
  • The method is successfully applied to ferromagnetic interactions, binary spin glasses, and Gaussian spin glasses.
  • The study shows how replica symmetry breaking can be incorporated.

Conclusions:

  • The cavity method provides an effective framework for analyzing metastable states in complex magnetic systems.
  • The presented method offers a versatile tool for studying various spin models.
  • The work highlights the importance of replica symmetry breaking for a complete description.