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Frustrated Ising systems on Husimi trees

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  • Monroe, James L.

Abstract

We consider two frustrated Ising model systems. The first is the full frustrated antiferromagnetic Ising model on the triangle lattice. We approximate the system by a Husimi tree. By a “sequential” build up of the tree we get a qualitatively correct phase diagram which quantitatively is close to other approximation methods. Most closed form approximations of this system such as mean field theory give qualitatively incorrect phase diagrams. As a further test of the Husimi tree approach we look at a frustrated Ising model on a checkerboard type lattice. This system has been solved exactly by Azaria et al., Phys. Rev. Lett. 59 (1987) 1629, when h=0. Again the Husimi tree approach gives qualitatively correct results approximating a rather complex phase diagram with e.g. reentrant phases. And in addition this approach allows one to determine the phase diagram for h≠0. Finally, this method should be easily extended to a number of other frustrated lattice spin systems such as the fully frustrated system on the simple cubic lattice.

Suggested Citation

  • Monroe, James L., 1998. "Frustrated Ising systems on Husimi trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 217-228.
    • Handle: RePEc:eee:phsmap:v:256:y:1998:i:1:p:217-228
    DOI: 10.1016/S0378-4371(98)00216-7
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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., 2016. "Exact results for the spin-1 Ising model on pure “square” Husimi lattices: Critical temperatures and spontaneous magnetization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 641-653.
    4. 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.
    5. Jurčišinová, E. & Jurčišin, M., 2017. "Evidence for the ferromagnetic frustration in a classical spin-1∕2 system with multisite interaction in external magnetic field: Exact results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 296-317.
    6. Jurčišinová, E. & Jurčišin, M., 2019. "Relevance of recursive lattice approximations for description of frustrated magnetic systems: Star kagome-like recursive lattice approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 330-351.

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