Relaxation dynamics near the order-disorder and order-order phase transitions in random crystal field Blume-Capel model

Abstract

The present study employs statistical equilibrium theory and irreversible thermodynamics to examine the relaxation dynamics of a spin-1 Blume-Capel model with a quenched random crystal field. First, the investigation focuses on the variation of the dipolar and quadrupolar order parameters as a function of the temperature and the crystal field within the mean-field approximation. It has been established that the mean-field equilibrium behavior of the model is characterized by phase diagrams exhibiting three distinct structures for varying values of the random fluctuation strength of the crystal field ($\alpha$) in the temperature versus crystal field plane. The induced novel phase resulting from disorders and the subsequent first-order phase transition at higher temperatures are highlighted through the dependence of the magnetization and quadrupole moment on the crystal field. It is assumed that the system has departed from equilibrium due to a small external magnetic field, a generalized force, and a current, all defined based on the production of magnetic Gibbs free energy, to formulate the relaxation behavior. The linearized kinetic equation was derived to determine the characteristic relaxation time. The relaxation time is demonstrated as a function of temperature and the crystal field for varying values of $\alpha$. The present study investigates the thermal and crystal field dependencies of relaxation times near critical, ordered critical, multicritical points, and first-order transitions. The characteristic relaxation time increases exponentially near the critical, tricritical, and isolated critical points, approaching an infinite duration.