Dynamics of the Blume-Capel model with quenched diluted single-ion anisotropy in the neighborhood of equilibrium states

The relaxation dynamics of a Blume-Capel model with a quenched diluted crystal field is formulated by a method combining the statistical equilibrium theory and the thermodynamics of linear irreversible processes. Using a mean-field approximation for the magnetic Gibbs free-energy production, a generalized force and a current are defined within the irreversible thermodynamics. Next the kinetic equation for the magnetization is obtained within linear response theory. Finally, the temperature dependence of the relaxation time in the neighborhood of the phase-transition points is obtained by solving the kinetic equation of the magnetization. We find that the relaxation time of the order parameter diverges near the critical and multicritical points, which corresponds to the familiar critical slowing down. On the other hand, it displays different behavior at the first-order phase transitions. It has a jump discontinuity at the first-order phase-transition temperatures. Moreover, the z dynamic critical exponent is calculated and compared with the z values obtained for a diverse class of systems, and good agreement is found with our results.