  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.
