Spin-lattice models: inhomogeneity and diffusion

In spin-lattice models with order parameter conserved, we generalize the idea of spin diffusion incorporating a variety factors as possible driving forces, including the external field and the temperature. The Kawasaki dynamics in the Gaussian model and the one-dimensional Ising model are studied. The Gaussian model is rigorously treated and the critical exponent $\gamma =1$ is obtained. The competition of the internal and the external inhomogeneities may lead to interesting and rich dynamic behavior. The diffusion induced by the inhomogeneity of the magnetization itself is believed to vanish near the critical point, meanwhile the nonvanishing diffusion induced by the inhomogeneity of the environment may be coupled to the spin configuration and weakened by thermal noise. Several interesting examples are visualized, and the concept of local hysteresis is proposed in this spin-conserved dynamics. A dynamic phase transition is observed in the one-dimensional Ising model subject to an electromagnetic wave.