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Mixed Spin-1/2 and Spin-5/2 Model by Renormalization Group Theory: Recursion Equations and Thermodynamic Study
Authors:A El Antari  H Zahir  A Hasnaoui  N Hachem  A Alrajhi  M Madani  M El Bouziani
Institution:1.Team of Theoretical Physics, Laboratory L.P.M.C., Department of Physics, Faculty of Sciences,Chouaib Doukkali University,El Jadida,Morocco;2.Laboratory LS3M, Polydisciplinary Faculty,Hassan I University,Khouribga,Morocco;3.Department of Physics and Chemistry,CRMEF,Meknès,Morocco;4.Department of Information Technologies, Faculty of Education and Applied Sciences,Hodeidah University,Raymah,Yemen
Abstract:Using the renormalization group approximation, specifically the Migdal-Kadanoff technique, we investigate the Blume-Capel model with mixed spins S = 1/2 and S = 5/2 on d-dimensional hypercubic lattice. The flow in the parameter space of the Hamiltonian and the thermodynamic functions are determined. The phase diagram of this model is plotted in the (anisotropy, temperature) plane for both cases d = 2 and d = 3 in which the system exhibits the first and second order phase transitions and critical end-points. 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. We have also presented a variation of the free energy derivative at the vicinity of the first and second order transitions. Finally, this work is completed by a discussion and comparison with other approximation.
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