Abstract
In this study, the mean-field approximation (MFA) is applied to the study of the XZ model for spin-1/2 in terms of Pauli spin matrices and their exponentials to obtain the magnetization components for the ferromagnetic (FM) and antiferromagnetic (AFM) cases. The details of obtaining the series expansion for the exponential Pauli spin matrices by using their fundamental properties and commutativity relations are presented. The partition function, free energy, and magnetization are obtained for a given coordination number in a simple form as hyperbolic tangent functions. The thermal variations of the magnetization components in the x- and z-directions are studied to obtain the phase diagrams in possible planes, which only present the second-order phase transitions. The reentrant behavior is also observed in the AFM case.
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