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The two-layer Ising model on a sequence of diamond-like hierarchical lattices

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  • Anisimova, G.D.
  • Myshlyavtsev, A.V.
  • Akimenko, S.S.

Abstract

The two-layer Ising model on diamond-like hierarchical lattices of different structures with equal fractal dimension was investigated. We applied the renormalization group transformations for the considered lattices. The critical values of the shift exponent φ were computed for various intralayer interaction values (J1 and J2). For the simplest diamond-like hierarchical lattice φ≈2.35 at J1=J2. As the structure of the lattice becomes more complex, the shift exponent value increases. At J1=0.5J2 the value φ≈0.5 was obtained, which is consistent with the data for the square lattice. The graphs of the heat capacity, magnetization and magnetic susceptibility were plotted at J1=0.5J2. They showed the absence of the second phase transition at an arbitrarily weak coupling between the layers.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:583:y:2021:i:c:s0378437121006142
    DOI: 10.1016/j.physa.2021.126341
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    References listed on IDEAS

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    1. Zhang, Yali & Wang, Jun, 2019. "Fluctuation entropy and complexity of financial percolation model with random jump on gasket fractal lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    2. Myshlyavtsev, A.V. & Myshlyavtseva, M.D. & Akimenko, S.S., 2020. "Classical lattice models with single-node interactions on hierarchical lattices: The two-layer Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    3. Ghaemi, Mehrdad & Ahmadi, Sheida, 2012. "Calculation of critical properties for the anisotropic two-layer Ising model on the Kagome lattice: Cellular automata approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2007-2013.
    4. Marčetić, Dušanka & Elezović-Hadžić, Sunčica & Živić, Ivan, 2020. "Statistics of close-packed dimers on fractal lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    5. Masrour, R. & Jabar, A., 2020. "Mixed spin-3/2 and spin-2 Ising model on diamond-like decorated square: A Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    6. Asgari, Yazdan & Ghaemi, Mehrdad, 2008. "Obtaining critical point and shift exponent for the anisotropic two-layer Ising and Potts models: Cellular automata approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 1937-1946.
    7. Horiguchi, Tsuyoshi & Tsushima, Norihiro, 1997. "Shift exponent and breakdown of universality for the two-layer Ising model on a square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 238(1), pages 295-306.
    8. Jabar, A. & Masrour, R., 2020. "Magnetic properties on a decorated triangular lattice: A Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    9. 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.
    10. Lipowski, A, 1998. "Critical temperature in the two-layered Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 373-383.
    11. Jabar, A. & Masrour, R., 2019. "Magnetic properties of Kekulene structure: A Monte Carlo study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 974-981.
    12. Canko, Osman & Kantar, Ersin & Keskin, Mustafa, 2009. "Nonequilibrium phase transition in the kinetic Ising model on a two-layer square lattice under the presence of an oscillating field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(1), pages 28-40.
    13. Jabar, A. & Masrour, R., 2019. "Magnetic properties of mixed spin-5/2 and spin-2 Ising model on a decorated square lattice: A Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 270-278.
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