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Phase transitions of the variety of random-field Potts models

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  • Türkoğlu, Alpar
  • Berker, A. Nihat

Abstract

The phase transitions of random-field q-state Potts models in d=3 dimensions are studied by renormalization-group theory by exact solution of a hierarchical lattice and, equivalently, approximate Migdal–Kadanoff solutions of a cubic lattice. The recursion, under rescaling, of coupled random-field and random-bond (induced under rescaling by random fields) coupled probability distributions is followed to obtain phase diagrams. Unlike the Ising model (q=2), several types of random fields can be defined for q≥3 Potts models, including random-axis favored, random-axis disfavored, random-axis randomly favored or disfavored cases, all of which are studied. Quantitatively very similar phase diagrams are obtained, for a given q for the three types of field randomness, with the low-temperature ordered phase persisting, increasingly as temperature is lowered, up to random-field threshold in d=3, which is calculated for all temperatures below the zero-field critical temperature. Phase diagrams thus obtained are compared as a function of q. The ordered phase in the low-q models reaches higher temperatures, while in the high-q models it reaches higher random fields. This renormalization-group calculation result is physically explained.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:583:y:2021:i:c:s0378437121006129
    DOI: 10.1016/j.physa.2021.126339
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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. Nihat Berker, A., 1993. "Critical behavior induced by quenched disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 72-76.
    3. 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.
    4. Rocha-Neto, Mário J.G. & Camelo-Neto, G. & Nogueira Jr., E. & Coutinho, S., 2018. "The Blume–Capel model on hierarchical lattices: Exact local properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 559-573.
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    1. Akın, Hasan & Ulusoy, Suleyman, 2023. "A new approach to studying the thermodynamic properties of the q-state Potts model on a Cayley tree," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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