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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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