IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v608y2022ip2s0378437122008585.html
   My bibliography  Save this article

Renormalization-group theory of the Heisenberg model in d dimensions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437122008585
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2022.128300?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. 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).
    3. 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).
    4. 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).
    5. 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).
    6. Liao, Yunhua & Aziz-Alaoui, M.A. & Zhao, Junchan & Hou, Yaoping, 2019. "The behavior of Tutte polynomials of graphs under five graph operations and its applications," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    7. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:608:y:2022:i:p2:s0378437122008585. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.