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Spin-glass phases and multichaos in the Ashkin–Teller model

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  • Saray, Alican
  • Berker, A. Nihat

Abstract

The global phase diagram of the Ashkin–Teller spin glass is calculated in d=3 spatial dimensions by renormalization-group theory. Depending on the value of the positive or negative four-spin interaction, qualitatively different topologies are found for the spin-glass phase diagram in the usual variables of temperature and fraction of antiferromagnetic nearest-neighbor interactions. Two different spin-glass phases occur. Both spin-glass phases are chaotic. One spin-glass exhibits phase reentrance that is reverse from the reentrances seen in previous spin-glass phase diagrams. Seven different phases: Ferromagnetic and antiferromagnetic, entropic ferromagnetic and entropic antiferromagnetic, spin-glass and entropic spin-glass, and disordered phases occur. The entropic ferromagnetic phase unusually but understandably occurs at temperatures above one spin-glass phase. A random disorder line is identified and no phase transition occurs on this line. Our calculation is exact on the d = 3 hierarchical lattice and Migdal–Kadanoff approximate on the cubic lattice.

Suggested Citation

  • Saray, Alican & Berker, A. Nihat, 2026. "Spin-glass phases and multichaos in the Ashkin–Teller model," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925014717
    DOI: 10.1016/j.chaos.2025.117458
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    References listed on IDEAS

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    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. Mirza, Fuat Kaan & Baykaş, Tunçer & Hekimoğlu, Mustafa & Pekcan, Önder & Tunçay, Gönül Paçacı, 2025. "Decoding rhythmic complexity: A nonlinear dynamics approach via visibility graphs for classifying asymmetrical rhythmic frameworks of Turkish classical music," Applied Mathematics and Computation, Elsevier, vol. 507(C).
    4. Zeynioğlu, Deniz Ipek & Berker, A. Nihat, 2025. "6-point tripled Ashkin–Teller global phase diagrams in two and three dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 680(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. 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).
    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).
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