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Thermodynamical behavior of the Blume–Capel model in the vicinity of its tricritical point

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  • Rocha-Neto, Mário J.G.
  • Camelo-Neto, G.
  • Nogueira, E.
  • Coutinho, S.

Abstract

We investigate the thermodynamic properties of the zero-field Blume–Capel model in the vicinity of its tricritical point (TCP). We calculate the internal energy, entropy, magnetization, quadrupole moment densities, and their response functions (specific heat and susceptibility) by employing an exact numerical recursion procedure for the model defined in a hierarchical lattice of fractal dimension d. We explore the scaling behavior of the isothermal and constant crystal-field-specific heat as a function of the temperature and the reduced crystal-field parameter along the ferromagnetic and the ordered paramagnetic phase frontier. Results achieved for systems with dimensions d=2 and 3 exhibit the main features of the continuous and first-order transitions in the TCP neighborhoods. We also probe the phase coexistence in the λ diagram and the latent heat in the neighborhood of the tricritical points locus.

Suggested Citation

  • Rocha-Neto, Mário J.G. & Camelo-Neto, G. & Nogueira, E. & Coutinho, S., 2023. "Thermodynamical behavior of the Blume–Capel model in the vicinity of its tricritical point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    • Handle: RePEc:eee:phsmap:v:629:y:2023:i:c:s0378437123007008
    DOI: 10.1016/j.physa.2023.129145
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    References listed on IDEAS

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    1. 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).
    2. 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.
    3. 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).
    4. Moonjung Jung & Dong-Hee Kim, 2017. "First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(12), pages 1-10, December.
    5. Curt Hagquist & Magnus Stenbeck, 1998. "Goodness of Fit in Regression Analysis – R 2 and G 2 Reconsidered," Quality & Quantity: International Journal of Methodology, Springer, vol. 32(3), pages 229-245, August.
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