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The two- and three-dimensional spin-3/2 random Blume–Capel model by the position space renormalization group

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  • El Bouziani, Mohammed
  • Gaye, Abou

Abstract

We use the Migdal–Kadanoff renormalization group technique to study the spin-3/2 Blume–Capel model under a random crystal field, in the two- and three-dimensional cases. Studying the fixed points and the phase diagrams established, we find interesting results allowing us to understand the critical behavior of the system. In the two-dimensional case, the randomness, even in small amounts, removes completely the first order transition between the two ferromagnetic phases present, replacing it by a smooth continuation. Only the second order phase transitions occur. In the three-dimensional case, the first order phase transition disappears only at a certain threshold of randomness. Below this threshold, we observe the presence of an end-point where finishes the first order transition line inside the ferromagnetic phases. This end-point reaches T=0K at a critical value of probability, beyond which only the second order transitions occur.

Suggested Citation

  • El Bouziani, Mohammed & Gaye, Abou, 2013. "The two- and three-dimensional spin-3/2 random Blume–Capel model by the position space renormalization group," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2643-2651.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:11:p:2643-2651
    DOI: 10.1016/j.physa.2013.02.003
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