Dynamics of a spin-1 Ising system in the neighborhood of equilibrium states - art. no. 026102

The dynamics of a spin-1 Ising system containing biquadratic interactions n ear equilibrium states is formulated by the method of thermodynamics of irr eversible processes. From the expression for the entropy production, genera lized forces and fluxes are determined. The kinetic equations are obtained by introducing kinetic coefficients that satisfy the Onsager relation. By s olving these equations a set of relaxation times is calculated and examined for temperatures near the phase transition temperatures, with the result t hat one of the relaxation times approaches infinity near the second-order p hase 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 temperatur e but displays a different behavior at the first-order phase transition, ju st a jump discontinuity. The behavior of both relaxation times is also inve stigated at the tricritical point. Moreover, the phase transition behaviors of the relaxation times are also obtained analytically via the critical ex ponents. Results are compared with conventional kinetic theory in the rando m-phase or generalized molecular-field approximation and a very good overal l agreement is found.