Magnetic Properties in the Spin-3/2 Ashkin-Teller Model from Mean Field Theory

In the present work, we investigate the spin-3/2 Ashkin-Teller model with on a cubic lattice with ferromagnetic coupling, utilizing mean field theory developed through a variational principle based on the Bogoliubov inequality to derive thermodynamic expressions, such as free energy and magnetization. We develop analytical equations and obtain numerical results, phase diagrams, and magnetizations, exploring different phases with continuous and first-order phase transitions, tricritical and bifurcation points. The different phases are obtained by considering a relationship between the couplings present in the model and the spin-3/2 anisotropy. Thermodynamic properties are characterized through the analysis of Hessian matrices, with an emphasis on the stable states of magnetizations. The results were compared with other works showing convergence and assimilating new characteristics in the study of the properties of this model, such as the presence of five distinct phases characterized by continuous and first-order phase transitions, tricritical and bifurcations points, in addition to the presence of new phases indicating the sensitivity of the system to variations in the exchange interaction values between the spin variables and the evolution of some phase transitions influenced by the spin-3/2 anisotropy.