Mixed spin-1/2 and spin-1 Ising model with uniaxial and biaxial single-ion anisotropy on the Bethe lattice

Abstract

Abstract:The mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial singleion anisotropy terms is solved exactly by combining star-triangle and triangle-star mapping transformations with exact recursion relations. Magnetic properties (magnetization, phase diagrams, and compensation phenomenon) are investigated in detail. Particular attention is focused on the effect of uniaxial and biaxial single-ion anisotropies that basically influence the magnetic behavior of the spin-1 atoms.PACS (

Spontaneous Magnetization and Phase Diagrams of the Mixed Spin-1/2 and Spin-S Ising Model on the Bethe Lattice

“…This qualitative difference appears owing to a sufficiently strong negative single-ion anisotropy D/J, which forces all integer spins towards their non-magnetic spin state S i = 0 and all half-odd-integer spins towards their lowest magnetic spin state S i = 1/2. Next, let us take a closer look at typical temperature variations of both sublattice magnetizations (m A , m B ) and total magnetization m T = (m A + m B )/2, which can be classified according to the extended Néel nomenclature [3,4]. It can be deduced from Fig.…”

“…From this point of view, our exact solution of the mixed-spin Ising model on the Bethe lattice is formally completed, since the exact results for the critical temperature and spontaneous magnetization of the spin-1/2 Ising model on the triangular Husimi lattice were already reported in Refs. [4,6]. For instance, the phase diagrams of the mixed-spin Ising model on the three-coordinated Bethe lattice can be obtained from a comparison of the effective interaction given by Eqs.…”

“…[4] one may extract exact results for the mixed-spin Ising model on the Bethe lattice from a rigorous mapping correspondence (7) with the spin-1/2 Ising model on the triangular Husimi lattice, which can be exactly treated by the method of exact recursion relations [5,6]. From this point of view, our exact solution of the mixed-spin Ising model on the Bethe lattice is formally completed, since the exact results for the critical temperature and spontaneous magnetization of the spin-1/2 Ising model on the triangular Husimi lattice were already reported in Refs.…”

“…For instance, the phase diagrams of the mixed-spin Ising model on the three-coordinated Bethe lattice can be obtained from a comparison of the effective interaction given by Eqs. (5), (6) with the critical value β c R = ln(7/3) [4], which provides the following critical condition: The similar procedure can be utilized for the exact calculation of both spontaneous sublattice magnetizations m A = σ j and m B = S i , which can be computed from the spontaneous magnetization of the spin-1/2 Ising model on the triangular Husimi lattice [6].…”

Critical properties of a random transverse crystal field Ising model with bond dilution

“…Htoutou et al have considered a ferromagnetic mixed Ising model with a transverse crystal field [15]. Ekiz et al have dealt with mixed spin-1/2 and spin-1 Ising models with uniaxial and biaxial single-ion anisotropy on the Bethe lattice [16]. It is worth noting that the model is a quantum Ising model.…”