The XYZ model in the mean-field approximation in terms of Pauli spin matrices

The mean-field approximation (MFA) of spin-1/2 XYZ model was studied by using the Pauli spin matrices and their exponentials which led to very nice hyperbolic tangent functions in nonlinear form. The magnetization components M x , M y and M z were obtained for the ferromagnetic (FM) case and then it was modified for the antiferromagnetic (AFM) case by introducing the sublattices. The bilinear exchange interaction parameters J x , J y and J z , and the external magnetic fields H x , H y and H z were considered along the three-dimensions for various coordination numbers q = 3, 4 and 6. The thermal variations of the magnetizations and thus the phase diagrams were obtained to illustrate the behaviours of phase transition lines in the AFM case.