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The Blume–Capel model on hierarchical lattices: Exact local properties

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

Abstract

The local properties of the spin one ferromagnetic Blume–Capel model defined on hierarchical lattices with dimension two and three are obtained by a numerical recursion procedure and studied as functions of the temperature and the reduced crystal-field parameter. The magnetization and the density of sites in the configuration S=0 state are carefully investigated at low temperature in the region of the phase diagram that presents the phenomenon of phase reentrance. Both order parameters undergo transitions from the ferromagnetic to the ordered paramagnetic phase with abrupt discontinuities that decrease along the phase boundary at low temperatures. The distribution of magnetization in a typical profile was determined on the transition line presenting a broad multifractal spectrum that narrows towards the fractal limit (single point) as the discontinuities of the order parameters grow towards a maximum. The amplitude of the order-parameter discontinuities and the narrowing of the multifractal spectra were used to delimit the low temperature interval for the possible locus of the tricritical point.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:494:y:2018:i:c:p:559-573
    DOI: 10.1016/j.physa.2017.11.156
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    1. Albayrak, Erhan, 2013. "Spin-1 Blume–Capel model with random crystal field effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 552-557.
    2. Rosas, Alexandre & Coutinho, Sérgio, 2004. "Random-field Ising model on hierarchical lattices: thermodynamics and ground-state critical properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 115-142.
    3. Madani, Mohamed & Gaye, Abou & El Bouziani, Mohamed & Alrajhi, Abdelhameed, 2015. "Migdal–Kadanoff solution of the mixed spin-1 and spin-3/2 Blume–Capel model with different single-ion anisotropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 396-404.
    4. Yüksel, Yusuf & Akıncı, Ümit & Polat, Hamza, 2012. "Critical behavior and phase diagrams of a spin-1 Blume–Capel model with random crystal field interactions: An effective field theory analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(9), pages 2819-2832.
    5. Siqueira, A.F. & Fittipaldi, I.P., 1986. "New effective-field theory for the Blume-Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(3), pages 592-611.
    6. Coutinho, S. & Donato Neto, O. & de Almeida, J.R.L. & Curado, E.M.F. & Morgado, W.A.M., 1992. "Multifractility of Ising models on hierarchical lattices: pure and spin glass cases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 271-277.
    7. Buzano, Carla & Pelizzola, Alessandro, 1995. "New topologies in the phase diagram of the semi-infinite Blume-Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 216(1), pages 158-168.
    8. El Bouziani, Mohammed & Gaye, Abou & Jellal, Ahmed, 2013. "Position space renormalization group study of the spin-1 random semi-infinite Blume–Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 689-701.
    9. Snowman, Daniel P., 2011. "A Blume–Capel spin glass with competing crystal-field interactions on a hierarchical lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1505-1515.
    10. Özkan, A. & Seferoğlu, N. & Kutlu, B., 2006. "Critical exponents of the three-dimensional Blume–Capel model on a cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 327-337.
    11. De Alcantara Bonfim, O.F., 1985. "Mean field renormalization group analysis of the Blume-Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 130(1), pages 367-373.
    12. Costabile, Emanuel & Roberto Viana, J. & Ricardo de Sousa, J. & Plascak, J.A., 2014. "The general-spin Blume–Capel model: A study of the multicritical behavior using effective-field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 297-303.
    13. Ekiz, Cesur & Keskin, Mustafa & Yalçın, Orhan, 2001. "Metastable and unstable states of the Blume–Capel model obtained by the cluster variation method and the path probability method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 215-232.
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