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The ferromagnetic q-state Potts model on three-dimensional lattices: a study for real values of q

Author

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  • Grollau, S.
  • Rosinberg, M.L.
  • Tarjus, G.

Abstract

We study the phase diagram of the ferromagnetic q-state Potts model on the various three-dimensional lattices for integer and non-integer values of q>1. Our approach is based on a thermodynamically self-consistent Ornstein–Zernike approximation for the two-point correlation functions. We calculate the transition temperatures and, when the transition is first order, the jump discontinuities in the magnetization and the internal energy, as well as the coordinates of the critical endpoint in external field. Our predictions are in very good agreement with the best available estimates. From the numerical study of the region of weak first-order transition, we estimate the critical value qc for which the transition changes from second- to first order. The q→1+ limit that describes the bond-percolation problem is also investigated.

Suggested Citation

  • Grollau, S. & Rosinberg, M.L. & Tarjus, G., 2001. "The ferromagnetic q-state Potts model on three-dimensional lattices: a study for real values of q," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 460-482.
    • Handle: RePEc:eee:phsmap:v:296:y:2001:i:3:p:460-482
    DOI: 10.1016/S0378-4371(01)00177-7
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    Cited by:

    1. Wang, Jie & Wang, Jun, 2020. "Cross-correlation complexity and synchronization of the financial time series on Potts dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

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