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Renormalization-group theory of the Heisenberg model in d dimensions

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  • Tunca, Egemen
  • Berker, A. Nihat

Abstract

The classical Heisenberg model has been solved in spatial d dimensions, exactly in d=1 and by the Migdal–Kadanoff approximation in d>1, by using a Fourier–Legendre expansion. The phase transition temperatures, the energy densities, and the specific heats are calculated in arbitrary dimension d. Fisher’s exact result is recovered in d=1. The absence of an ordered phase, conventional or algebraic (in contrast to the XY model yielding an algebraically ordered phase) is recovered in d=2. A conventionally ordered phase occurs at d>2. This method opens the way to complex-system calculations with Heisenberg local degrees of freedom.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:608:y:2022:i:p2:s0378437122008585
    DOI: 10.1016/j.physa.2022.128300
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    References listed on IDEAS

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    1. 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).
    2. Ma, Fei & Su, Jing & Hao, Yongxing & Yao, Bing & Yan, Guanghui, 2018. "A class of vertex–edge-growth small-world network models having scale-free, self-similar and hierarchical characters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1194-1205.
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    Cited by:

    1. Rocha-Neto, Mário J.G. & Camelo-Neto, G. & Nogueira, E. & Coutinho, S., 2023. "Thermodynamical behavior of the Blume–Capel model in the vicinity of its tricritical point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).

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