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Physical review. B, Condensed matter

Mixed-spin Ising model on the Bethe lattice

N. R. da Silva, Silvio R. A. Salinas

Published Jul 1, 1991• 57 citations
Publisher

Abstract

We obtain the phase diagram of a ferromagnetic mixed Ising system, consisting of spin-1/2 and spin-S variables, on a Bethe lattice of coordination number z, with nearest-neighbor exchange interactions and single-ion terms. The problem is formulated as a discrete nonlinear map. There is a tricritical point for S integer and z\ensuremath{\ge}5. In the infinite-coordination-number limit, we regain the results of an exact calculation for a Curie-Weiss version of the model.

DOI
10.1103/physrevb.44.852

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We obtain the phase diagram of a ferromagnetic mixed Ising system, consisting of spin-1/2 and spin-S variables, on a Bethe lattice of coordination number z, with nearest-neighbor exchange interactions and single-ion terms. The problem is formulated as a discrete nonlinear map. There is a tricritical point for S integer and z\ensuremath{\ge}5. In the infinite-coordination-number limit, we regain the results of an exact calculation for a Curie-Weiss version of the model.
MIXED SPIN-1 AND SPIN-32\frac{3}{2}23​ BLUME–CAPEL ISING FERRIMAGNETIC SYSTEM ON THE BETHE LATTICE
The mixed spin-1 and spin-[Formula: see text] Blume–Capel Ising ferrimagnetic system for the central spin with spin-1 is studied on the Bethe lattice using the exact recursion equations. The exact expressions for the magnetization, the quadrupolar moment, the Curie temperature and the free energy are found and the phase diagrams are constructed on the Bethe lattice with the coordination numbers q = 3, 4 and 6 for the various values of the single-ion anisotropy constants dA = DA/J for spin-1 and dB = DB/J for spin-[Formula: see text]. The existence of a tricritical point is investigated for different values of q and the single-ion anisotropy constants. The phase diagrams in the (kTc/J, dA) plane for the central spin are obtained for two different cases; (1) dA = dB and (2) dA is varied for selected values of dB. The results are compared with those of other approximate methods.
The effect of uniaxial single-ion anisotropy on magnetic and critical properties of the mixed spin-1/2 and spin-S (S > 1/2) Ising model on a three-coordinated Bethe lattice is rigorously examined with the help of star-triangle transformation and exact recursion relations.In particular, our attention is focused on the ferrimagnetic version of the model, which exhibits diverse temperature dependences of the total and both sublattice magnetizations.It is shown that the critical behavior of the mixed-spin Ising model on the Bethe lattice basically depends on whether the quantum spin number S is integer or half-odd-integer.
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