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Frustrations on decorated triangular lattice in Ising model

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  • Kassan-Ogly, F.A.
  • Zarubin, A.V.

Abstract

We study the frustration properties of the Ising model on a decorated triangular lattice with an arbitrary number of decorating spins on all lattice bonds in the framework of an exact analytical approach based on the Kramers–Wannier transfer matrix method. Expressions for the entropy, heat capacity, and spontaneous magnetization of the lattice are obtained, including the residual (zero-temperature) entropy and residual (zero-temperature) spontaneous magnetization of the system. The existence of magnetic frustrations in such a model and their influence on the behavior of the thermodynamic functions of the system are shown. The new and most important result of our study is related to the description of the possible coexistence of frustrations and long-range magnetic order in partially ordered spin systems.

Suggested Citation

  • Kassan-Ogly, F.A. & Zarubin, A.V., 2023. "Frustrations on decorated triangular lattice in Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 627(C).
    • Handle: RePEc:eee:phsmap:v:627:y:2023:i:c:s037843712300691x
    DOI: 10.1016/j.physa.2023.129136
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    References listed on IDEAS

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    1. Valverde, J.S. & Rojas, Onofre & de Souza, S.M., 2008. "Geometric frustration in Ising diamond chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 1947-1956.
    2. Pires, A.S.T., 2012. "Frustration in the anisotropic XY model on a triangular lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5433-5438.
    3. 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.
    4. Si, Nan & Su, Xin & Meng, Jing & Miao, Hai-Ling & Zhang, Yan-Li & Jiang, Wei, 2020. "Magnetic properties of decorated 2D kagome-like lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    5. Kaneyoshi, T., 1997. "A note on a decorated ferrimagnetic Ising system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(3), pages 554-572.
    6. Monroe, James L., 1998. "Frustrated Ising systems on Husimi trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 217-228.
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