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Classical lattice models with single-node interactions on hierarchical lattices: The two-layer Ising model

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  • Myshlyavtsev, A.V.
  • Myshlyavtseva, M.D.
  • Akimenko, S.S.

Abstract

A general approach is proposed for renormalization group transformations at arbitrary hierarchical lattices with two root nodes and the presence of single-node interactions (interactions between layers, magnetic field, chemical potential, etc.). The effectiveness of the proposed approach was shown for the two-layer Ising model in a zero magnetic field on the simplest representative of folded square hierarchical lattices. The phase diagram was investigated and the shift exponent (φ) was calculated at various values of the interaction energy in each layer (J1,J2) and between the layers (J3). The value φ≈ 2.41 was obtained for identical interactions in the layers (J1= J2). In the remaining cases (J1≠J2) the shift exponent turned out to be close to 0.5, which is consistent with the data for the square lattice. The exceptional case is J1 > 0, J2> 0, and J1 ≠J2, where the transition shift exponent in the second layer takes the value 2.57.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120304751
    DOI: 10.1016/j.physa.2020.124919
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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).
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    Cited by:

    1. Türkoğlu, Alpar & Berker, A. Nihat, 2021. "Phase transitions of the variety of random-field Potts models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    2. Keçoğlu, Ibrahim & Berker, A. Nihat, 2023. "Global Ashkin–Teller phase diagrams in two and three dimensions: Multicritical bifurcation versus double tricriticality—endpoint," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    3. 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).
    4. Tunca, Egemen & Berker, A. Nihat, 2022. "Renormalization-group theory of the Heisenberg model in d dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P2).
    5. Artun, E. Can & Keçoğlu, Ibrahim & Türkoğlu, Alpar & Berker, A. Nihat, 2023. "Multifractal spin-glass chaos projection and interrelation of multicultural music and brain signals," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    6. Pektaş, Yiğit Ertaç & Artun, E. Can & Berker, A. Nihat, 2023. "Driven and non-driven surface chaos in spin-glass sponges," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    7. Artun, E. Can & Sarman, Deniz & Berker, A. Nihat, 2024. "Nematic phase of the n-component cubic-spin spin glass in d = 3: Liquid-crystal phase in a dirty magnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).

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