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Phase diagrams of the q-state potts model on Bethe lattices

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  • Peruggi, Fulvio
  • di Liberto, Francesco
  • Monroy, Gabriella

Abstract

We use a rigorous, recently developed, method of solution of spin models on Bethe lattices (Cayley trees). It allows us to detect all the phases of the ferromagnetic and antiferromagnetic q-state Potts models in a field (FPM and APM respectively). The phase diagrams of the FPM are characterized by three critical lines of first-order transitions. In the APM the ordered phases (which appear always for h > 0, and under certain conditions for h= 0 and/or h<0) are separated from the disordered one by phase boundaries characterized by second-order transitions, and are separated one from the other by critical lines characterized by first-order and second-order transitions. Several results are found, which hold true on standard lattices, too.

Suggested Citation

  • Peruggi, Fulvio & di Liberto, Francesco & Monroy, Gabriella, 1987. "Phase diagrams of the q-state potts model on Bethe lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 141(1), pages 151-186.
    • Handle: RePEc:eee:phsmap:v:141:y:1987:i:1:p:151-186
    DOI: 10.1016/0378-4371(87)90267-6
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    References listed on IDEAS

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    1. Peruggi, Fulvio & di Liberto, Francesco & Monroy, Gabriella, 1984. "Some AB-percolation problems in the antiferromagnetic potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(1), pages 175-190.
    2. Peruggi, Fulvio & Di Liberto, Francesco & Monroy, Gabriella, 1985. "Critical behaviour in three-state Potts antiferromagnets on a Bethe lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 131(1), pages 300-310.
    3. G. J. Schick & B. F. Kunnecke, 1982. "Do High Grades, Top Schools, or An Advanced Degree Lead to Job Security and Extraordinary Salary Progression?," Interfaces, INFORMS, vol. 12(1), pages 9-18, February.
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    Cited by:

    1. Bakchich, A. & Benyoussef, A. & Touzani, M., 1993. "Antiferromagnetic Potts model in a magnetic field: a finite size scaling study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 192(3), pages 516-524.
    2. Peruggi, Fulvio, 1987. "First-order transitions in percolation models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 141(1), pages 140-150.
    3. Nardi, Francesca R. & Zocca, Alessandro, 2019. "Tunneling behavior of Ising and Potts models in the low-temperature regime," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4556-4575.
    4. Bet, Gianmarco & Gallo, Anna & Nardi, F.R., 2024. "Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics," Stochastic Processes and their Applications, Elsevier, vol. 172(C).

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