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Replica symmetry breaking in the Ising spin glass model on Bethe-like lattices with loop

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  • Yokota, Terufumi

Abstract

The Ising spin glass model on Bethe-like lattices (cactus lattices) is studied using replicas in the presence of a magnetic field. Parisi's order parameter function and the de Almeida–Thouless (AT) line are obtained close to the spin glass transition temperature. The results are compared with those for the Bethe lattice to see the effects of loops. The slope of the order parameter function diminishes considerably for both lattices compared with that for the Sherrington–Kirkpatrick (SK) model. The loci of the AT line for the cactus lattices and the Bethe lattice are above and below that for the SK model, respectively.

Suggested Citation

  • Yokota, Terufumi, 2007. "Replica symmetry breaking in the Ising spin glass model on Bethe-like lattices with loop," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 534-544.
    • Handle: RePEc:eee:phsmap:v:379:y:2007:i:2:p:534-544
    DOI: 10.1016/j.physa.2006.11.094
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    Cited by:

    1. Jurčišinová, E. & Jurčišin, M., 2019. "Entropy properties of antiferromagnetic model on kagome lattice: Effective-field theory approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    2. Jurčišinová, E. & Jurčišin, M., 2014. "The first order phase transitions in the multisite spin-1/2 model on a pure Husimi lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 375-385.
    3. Jurčišinová, E. & Jurčišin, M., 2019. "Applicability of effective field theory cluster approximations for investigation of geometrically frustrated magnetic systems: Antiferromagnetic model on kagome lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 644-657.

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