Phase diagrams and the thermal variations of the order‐parameters in the mixed spin‐1 and spin‐$3 \over 2$ ising model on the Bethe lattice

Abstract

The mixed spin-1 and spin- Ising system using the exact recursion relations, but one with the central-spin with spin-1 and the other is for the central-spin with spin-3 2 for q ¼ 3, thus, it is shown that the choice of the central-spin on the Bethe lattice has no effect on the phase diagrams.

The possibility of two compensation points in a ferrimagnetic mixed spin-1 and spin-3/2 Ising system using Bethe lattice approach

“…The critical phenomena of the mixed spin-1 and spin-3/2 Ising model, which takes into account the influence of a crystal field or transverse field was examined by various methods, e.g., the effective-field theory with correlations (EFT) [11][12][13][14][15][16], the cluster variation method with the pair approximation (CVMPA) [17], the mean-field approximation (MFA) [18] and the Bethe lattice solution [19,20]. Some of them indicate the existence of the compensation points in the system with S ¼ 1 and coordination number q ¼ 6.…”

The mixed-spin ternary-alloy in the form of ABpC1−p on the Bethe lattice

“…It is clear that when p¼1, this model reduces to the mixed spin-(1, 3 2 ) model [26], while for p¼0 or q¼1, it corresponds to mixed spin-ð 3 2 , 5 2 Þ model [27] (see also the references therein). Therefore, for the formulation of the ternaryalloy, we have to consider the mixed spin-(1, 3 2 ) and spin-ð 3 2 , 5 2 Þ models separately and then combine them appropriately.…”

“…1. Thus for the mixed spin-ð 3 2 ,1Þ model [26] with spin-3/2 as the central spin and spin-1 as the NN spin, one can obtain three recursion relations for spin-3/2 as…”

The mixed‐spin ferro–ferrimagnetic ternary alloy

“…(2). Therefore, it is obvious that when p = 1 or q = 0 this model reduces to the mixed spin‐(1, 3/2) model 22, while for p = 0 or q = 1 it corresponds to mixed spin‐(1, 1/2) model 23.…”

“…1. Thus for the mixed spin‐(1, 3/2) model 22 with spin‐1 as the central spin and spin‐3/2 as the NN spin, one can obtain two recursion relations for spin‐1 as and three recursion relations for the spin‐3/2 as where $R = |J_{{\rm AB}} |/J_{{\rm AC}} $ and $\beta ' = \beta |J_{{\rm AC}} |$ .…”