Relaxation phenomena in the Blume–Emery–Griffiths model near the critical and multicritical points

Abstract

The relaxation behaviour of the Blume-Emery-Griffiths (BEG) model Hamiltonian with bilinear and biquadratic nearest-neighbour ferromagnetic exchange interaction and crystal field interactions is studied by using the molecular field approximation (MFA) and Onsager's theory of irreversible thermodynamics. First the equilibrium behaviour and the phase diagrams of the model in MFA are given briefly in order to understand the relaxation behaviour. Then, Onsager theory is applied to the model and the set of linear differential equations, which is also called the kinetic or rate equations, is obtained. By solving these equations a set of relaxation times is calculated and examined for temperatures near the critical and multicritical points. It is found that one of the relaxation times 1 ( ) τ is sharply cusped at the triple and critical points, whereas it approaches infinity near the critical-end point. On the other hand, the other relaxation time 2 ( ) τ displays a jump-discontinuity behaviour at the triple and critical points but it has a cusp at the critical-end point. A maximum of 2 τ has also been observed above the critical-end point. Moreover, similar calculations are performed for non-zero magnetic field (H) to investigate the effect of H on relaxation times.

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

“…In agreement with the results of the present work, it is observed in Refs. [28,53] that one of the relaxation times exhibits a divergence in the vicinity of CEP and DCP. Consequently, the Blume-Capel model with random single-ion isotropy exhibits critical slowing down at the critical, tricritical, critical end, and double critical endpoints.…”

“…The Blume-Emery-Griffiths model is investigated for CEP in Ref. [53]. Later, Gulpinar et al studied the metamagnetic Ising model for both CEP and DCP [28].…”

Magnetic relaxation in a spin-1 Ising model near the second-order phase transition point

“…For the dynamical aspects of phase transitions we have used the linear kinetic equations for the long-range order parameters to derive relaxation times on the basis of Onsager theory of irreversible thermodynamics [30][31][32][33]. We have also derived the sound attenuation coefficient and velocity dispersion relation to investigate the properties of ultrasound propagation near the phase transition temperatures [34][35][36][37].…”

Slow and fast relaxation times of quantum lattice model with local multi-well potentials: phenomenological dynamics for Sn2P2S6 ferroelectric crystals

“…In this work, we have made use of a simple phenomenological way to define the slow and fast relaxation times near the ferroelectric phase transitions in the SPS crystals. Such a study of relaxation dynamics has already been presented to observe the time dependent behaviours near the phase transitions and critical phenomena in various systems [27][28][29][30][31][32][33][34][35].…”