Abstract
We study the mixed spin-1 and spin-3/2 Blume-Capel model under 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. As a function of the ratio R of bulk and surface interactions and the ratios R1 and R2 of bulk and surface crystals fields on the spin-1 and spin-3/2 respectively, we have determined various types of phase diagrams. Besides second- order transition lines, first-order phase transition lines terminating at tricritical points are obtained. We found that there existed nine main types of phase diagram showing a variety of phase transitions associated with the surface, including ordinary, extraordinary, surface and special phase transitions.
Highlights
The problems of surface magnetism have been investigated for many years
The system of mixed spins S = 1/2 and S = 1 has been one of the simplest to be studied early and largely, namely by the techniques of renormalization group [32] [33], the Bethe-Peierls approximation [34], the effective field theory [35] [36], the MonteCarlo simulation [37] [38] and the finite cluster approximation [39]. This attention has been expanded on systems of mixed spins higher than 1/2, like the case S = 1 and S = 3/2, which has been studied by several methods, as the mean field approximation (MF) [40], the Bethe lattice recursion relations [41] [42], the effective field theory [43] [44], the Monte-Carlo simulation [45], the Green’s function [46], the recursion relations on Cayley tree [47] and the real space renormalization group theory [48]. Our aim in this present paper is to determine the various types of phase diagram in the semi-infinite system of mixed spins S = 1 and S = 3/2 on the Blume-Capel model [28] [29], which we study by using a renormalization group (RG) method, namely the Migdal-Kadanoff one [49] [50], combining the decimation as well as the bond shifting
We have studied the pure Blume-Capel model in the semi-infinite case
Summary
The problems of surface magnetism have been investigated for many years. Among them the effects of surface on phase transitions in semi-infinite systems have received increasing interest. This attention has been expanded on systems of mixed spins higher than 1/2, like the case S = 1 and S = 3/2, which has been studied by several methods, as the mean field approximation (MF) [40], the Bethe lattice recursion relations [41] [42], the effective field theory [43] [44], the Monte-Carlo simulation [45], the Green’s function [46], the recursion relations on Cayley tree [47] and the real space renormalization group theory [48] Our aim in this present paper is to determine the various types of phase diagram in the semi-infinite system of mixed spins S = 1 and S = 3/2 on the Blume-Capel model [28] [29], which we study by using a renormalization group (RG) method, namely the Migdal-Kadanoff one [49] [50], combining the decimation as well as the bond shifting.
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