Kinetic Ising Model with the Bilinear and Biquadratic Interactions

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Abstract
Using a conventional kinetic theory dynamical behaviours of the spin-one Ising system containing the biquadratic interaction are investigated for various values of the ratio of the bilinear to biquadratic interaction. Expectation values of the dipolar and quadrupolar moment are solved from equations derived in the molecular-field approximation, and their changes near equilibrium in each phase are shown to be described by two characteristic time constants which vary with temperature in different ways. Nonequilibrium relaxations of the system are also investigated numerically in several cases. A remarkable feature is found in flatness property of the expectation values when they approach to the paramagnetic values at temperatures just above the transition temperature of the first-order quadrupolar or ferromagnetic phase transition.