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The bilayer Ising model and a generalized Husimi tree approximation

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  • Monroe, James L

Abstract

We study a variety of aspects of a bilayer system of Ising spins including accurate estimates of the critical temperature for ferromagnetic interactions, scaling of the critical temperature when the interlayer interaction goes to zero, and approximations of phase diagrams for the case when antiferromagnetic interlayer interactions are present including location of the tricritical point. This is all done using an extension of a method previously developed by the author to study a variety of lattice spin systems and which is a generalization of the Bethe lattice approach.

Suggested Citation

  • Monroe, James L, 2004. "The bilayer Ising model and a generalized Husimi tree approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 563-576.
    • Handle: RePEc:eee:phsmap:v:335:y:2004:i:3:p:563-576
    DOI: 10.1016/j.physa.2003.12.018
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    Cited by:

    1. 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.
    2. Anisimova, G.D. & Myshlyavtsev, A.V. & Akimenko, S.S., 2021. "The two-layer Ising model on a sequence of diamond-like hierarchical lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    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.
    4. Moodie, Jordan C. & Kainth, Manjinder & Robson, Matthew R. & Long, M.W., 2020. "Transition temperature scaling in weakly coupled two-dimensional Ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

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