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Loop effects in the Ising spin glass on the Bethe-like lattices

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  • Yokota, Terufumi

Abstract

Equations for the spin glass order in the Ising spin glass model on the Bethe-like lattices with and without small loops are studied. For each lattice, equations are obtained by using and not using the replica method. Within the replica symmetric approximation, equations obtained by the two ways are shown to be identical. To see the effects of the small loops and the replica symmetry breaking, a spin glass order parameter is investigated as a function of the connectivity of the lattices close to the transition temperature. Replica symmetry breaking is enhanced by the existence of small loops.

Suggested Citation

  • Yokota, Terufumi, 2008. "Loop effects in the Ising spin glass on the Bethe-like lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3495-3502.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:14:p:3495-3502
    DOI: 10.1016/j.physa.2008.02.022
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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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