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XY-Ashkin–Teller phase diagram in d=3

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  • Türkoğlu, Alpar
  • Berker, A. Nihat

Abstract

The phase diagram of the Ashkin-Tellerized XY model in spatial dimension d=3 is calculated by renormalization-group theory. In this system, each site has two spins, each spin being an XY spin, that is having orientation continuously varying in 2π radians. Nearest-neighbor sites are coupled by two-spin and four-spin interactions. The phase diagram has ordered phases that are ferromagnetic and antiferromagnetic in each of the spins, and phases that are ferromagnetic and antiferromagnetic in the multiplicative spin variable. The phase diagram distinctively exhibits a pair of symmetrically situated direct bifurcation points and a pair of symmetrically situated reverse bifurcation points of the phase boundaries. The renormalization-group flows are in terms of the doubly composite Fourier coefficients of the exponentiated energy of nearest-neighbor spins.

Suggested Citation

  • Türkoğlu, Alpar & Berker, A. Nihat, 2025. "XY-Ashkin–Teller phase diagram in d=3," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 674(C).
    • Handle: RePEc:eee:phsmap:v:674:y:2025:i:c:s037843712500367x
    DOI: 10.1016/j.physa.2025.130715
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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. 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. 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. 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. 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).
    6. 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.
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