Critical and multicritical behaviors of static and complex magnetic susceptibilities for the mean-field Blume-Capel model with a random crystal field

The static and dynamic linear response functions for the spin-1 mean-field Blume-Capel model with a random diluted single-ion anisotropy are derived using the thermodynamics of linear irreversible processes. Thermal dependence of the static susceptibility is studied in detail. In addition, by utilizing the stationary solution of the kinetic equation in existence of sinusoidal external magnetic field, the low frequency thermal behavior of the magnetic absorption and dispersion factors are investigated. Particularly, we have analyzed the behaviors of these quantities near both first- and second-order transition temperatures and multicritical points such as tricritical point, critical endpoint and double critical endpoint. The static and dynamical mean field critical exponents in hydrodynamic limit are also calculated in order to formulate the critical and multicritical behaviors of the magnetic susceptibility. Finally, a comparison of the findings of this study with previous theoretical and experimental studies is presented and it is shown that a good agreement is found with our results.