IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v630y2023ics0378437123008038.html
   My bibliography  Save this article

Global Ashkin–Teller phase diagrams in two and three dimensions: Multicritical bifurcation versus double tricriticality—endpoint

Author

Listed:
  • Keçoğlu, Ibrahim
  • Berker, A. Nihat

Abstract

The global phase diagrams of the Ashkin–Teller model are calculated in d=2 and 3 by renormalization-group theory that is exact on the hierarchical lattice and approximate on the recently improved Migdal–Kadanoff procedure. Three different ordered phases occur in the dimensionally distinct phase diagrams that reflect three-fold order-parameter permutation symmetry, a closed symmetry line, and a quasi-disorder line. First- and second-order phase boundaries are obtained. In d=2, second-order phase transitions meeting at a bifurcation point are seen. In d=3, first- and second-order phase transitions are separated by tricritical and critical endpoints.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:630:y:2023:i:c:s0378437123008038
    DOI: 10.1016/j.physa.2023.129248
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123008038
    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.2023.129248?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. 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. 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. Clark, Jeremy & Lochridge, Casey, 2023. "Weak-disorder limit for directed polymers on critical hierarchical graphs with vertex disorder," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 75-102.
    Full references (including those not matched with items on IDEAS)

    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 & 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).
    2. 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).
    3. 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).
    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. 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).
    6. 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).
    7. 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).

    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:630:y:2023:i:c:s0378437123008038. 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.