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Finite Temperature Phase Diagrams of the Mixed Spin-1 and Spin-2 Blume–Capel Model by Renormalization Group Approach

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Abstract

The Blume–Capel model with mixed spins S = 1 and S = 2, on d-dimensional hypercubic lattice, is studied using the real space renormalization group approximation and specifically the Migdal–Kadanoff technique. We give the phase diagrams on the (Δ1/|J|, 1/|J|) and (Δ2/|J|, 1/|J|) planes which are studied for selected values of Δ2/|J| and Δ1/|J| respectively, with first and second order phase transitions and tricritical points. Also, the associated fixed points are drawn up in a table, and by linearizing the transformation at the vicinity of these points, we determine the critical exponents for d = 2 and d = 3. In particular, we find that the system under study may exhibit reentrant phenomenon.

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Authors and Affiliations

  1. Equipe de Physique Théorique Laboratoire L.P.M.C, Département de Physique, Faculté des Sciences, Université Chouaib Doukkali, B.P. 20 24000, El Jadida, Morocco

    A. Lafhal, N. Hachem, H. Zahir, M. El Bouziani & A. Alrajhi

  2. Département de Physique-Chimie, CRMEF, Meknès, Morocco

    M. Madani

  3. Laboratoire LS3M, Faculté Polydisciplinaire, Université Hassan I, Khouribga, Morocco

    H. Zahir

  4. Department of Information Technologies, Faculty of Education and Applied Sciences, Hodeidah University, Raymah, Yemen

    A. Alrajhi

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  1. A. Lafhal
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  2. N. Hachem
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  3. H. Zahir
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  4. M. El Bouziani
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  5. M. Madani
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Correspondence to M. El Bouziani.

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Lafhal, A., Hachem, N., Zahir, H. et al. Finite Temperature Phase Diagrams of the Mixed Spin-1 and Spin-2 Blume–Capel Model by Renormalization Group Approach. J Stat Phys 174, 40–55 (2019). https://doi.org/10.1007/s10955-018-2172-0

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