Dynamics of a spin-1 Ising system in the neighborhood of equilibrium states

Abstract

The dynamics of a spin-1 Ising system containing biquadratic interactions near equilibrium states is formulated by the method of thermodynamics of irreversible processes. From the expression for the entropy production, generalized forces and fluxes are determined. The kinetic equations are obtained by introducing kinetic coefficients that satisfy the Onsager relation. By solving these equations a set of relaxation times is calculated and examined for temperatures near the phase transition temperatures, with the result that one of the relaxation times approaches infinity near the second-order phase transition temperature on either side, whereas it is sharply cusped at the first-order phase transition temperature. On the other hand, the other relaxation time has a cusp at the second-order phase transition temperature but displays a different behavior at the first-order phase transition, just a jump discontinuity. The behavior of both relaxation times is also investigated at the tricritical point. Moreover, the phase transition behaviors of the relaxation times are also obtained analytically via the critical exponents. Results are compared with conventional kinetic theory in the random-phase or generalized molecular-field approximation and a very good overall agreement is found.

Frequency dependence of the complex susceptibility for a spin-1 Ising model

“…These equations are found and given in Refs. [7][8][9][10][11] explicitly. To derive an expression for the CS of the system, we first have to consider the case in which the lattice is stimulated by a small uniform external magnetic field H oscillating at an angular frequency o and obtain the complex susceptibility (w).…”

“…(5), the relaxation times t 1 and t 2 are obtained by considering the corresponding homogeneous kinetic equations resulting when there is no external stimulation, i.e. H ¼ 0 [7][8][9][10][11].…”

“…The relaxation process and sound propagation in the system were studied by using the flows in order parameters [7][8][9][10]. Recently, complex susceptibility (CS) or dynamic susceptibility for the same model Hamiltonian was also investigated and only the critical behaviors for the dispersion and absorption components were presented by us [11].…”

Nonequilibrium Thermodynamics of Ising Magnets

“…For the ferromagnetic interaction, a short range order parameter as well as the long range order is introduced (Tanaka et al, 1962;Barry, 1966) while there are two long range sublattice magnetic orders and a short range order in the Ising antiferromagnets (Barry & Harrington, 1971). Similarly the number of thermodynamic variables (order parameters) also increases when the higher order interactions are considered (Erdem & Keskin, 2001;Gülpınar et al, 2007;Canko & Keskin, 2010). For a general formulation of Ising spin kinetics with a multiple number of spin orderings ( i  ), the Gibbs free energy production is written …”

Magnetic Properties and Size Effects of Spin-1/2 and Spin-1 Models of Core-Surface Nanoparticles in Different Type Lattices

“…Ising models (Erdem, 1995;Keskin, & Erdem 1997;Erdem & Keskin, 2001;Erdem, 2009;Erdem, 2008;Chen & Levy, 1973) and thier variants such as Blume-Capel (Blume, 1966;Capel, 1966;Bakchich, et al, 1994), Blume-Emery-Griffiths (Blume, et al, 1971;Achiam, 1985;Hoston, & Berker, 1991;Bakkali, 1996;Goveas & Mukhopadhyay, 1997;Keskin, et al, 1999;Temizer, 2008) and mixed spin (Benayad & Dakhama 1997;Kaneyoshi, 1998;Albayrak, & Yigit, 2005;Albayrak, & Yigit, 2006;) models were regarded as theoretical simplifications, designed to model the essential aspects of cooperative system (Kikuchi,1951) without detailed correspondence to specific materials.…”