Abstract
A two-fold Cayley tree with fully q-coordinated sites is constructed and the spin-1 Blume–Capel model in the presence of an external magnetic field is solved exactly. The relevant properties such as magnetization m and square magnetic moment q are investigated as functions of temperature and external magnetic field both for ferromagnetic and antiferromagnetic couplings. In the study, we propose a possible mechanism of the plateau based on the exchange couplings.
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