Abstract
The magnetic properties of the mixed spin-$\frac{1}{2}$ and spin-$\frac{7}{2}$ Ising model with a crystal-field in a longitudinal magnetic field are investigated on the Bethe lattice using exact recursion relations. The ground-state phase diagram is constructed. The temperature-dependent one is displayed in the case of uniform crystal-field on the $(k_{\text{B}}T/|J|, D/|J|)$ plane in the absence of the external constraint for lattice coordination numbers $z = 3, 4, 6$. The order parameters and corresponding response functions as well as the internal energy are calculated and examined in detail in order to feature the real nature of phase boundaries and corresponding temperatures. The thermal variations of the average magnetization are classified according to the N\'{e}el nomenclature.
Highlights
The investigation of mixed Ising systems has been of great interest in statistical mechanics during the past decades [1–4]
This is due to the revelation of novel critical magnetic properties not detected during studies of their single-spin counterparts
It is important to indicate that in the case of h/|J | = 0, the model exhibits the second-order transition at a Curie temperature Tc/|J | = 3.110, where the two sublattice magnetizations continuously go to zero after decreasing from their saturation values at T = 0
Summary
The investigation of mixed Ising systems has been of great interest in statistical mechanics during the past decades [1–4] This is due to the revelation of novel critical magnetic properties not detected during studies of their single-spin counterparts. These systems are used to model ferrimagnetic materials whose properties are often needed in modern sophisticated technologies, such as magnetic recording, storage and reading devices [5–11] Such systems have been studied by several statistical mechanical methods: renormalization-group technique [12, 13], mean-field approximation [14–18], effective-field theory [19–24], Monte Carlo simulations [25–29]. By means of the effective-field theory, Essaoudi et al [31] studied the same model using a probability distribution technique This investigation revealed a remarkable influence of the field strength on the magnetic properties of this system.
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