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Position space renormalization group study of the spin-1 random semi-infinite Blume–Capel model

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  • El Bouziani, Mohammed
  • Gaye, Abou
  • Jellal, Ahmed

Abstract

We study the spin-1 Blume–Capel model under a random crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal–Kadanoff technique. Interesting results are obtained, which tell us that the randomness destroys the first order phase transitions and only those of the second order occur. We give the list of nine fixed points and their topology describing the surface critical behavior. Five new types of phase diagram are found with a rich variety of phase transitions, in accordance with the values of the bulk and surface probabilities and the ratios linking bulk and surface interactions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:689-701
    DOI: 10.1016/j.physa.2012.10.007
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    Cited by:

    1. 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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