EXTENDED KINETIC ISING-MODEL AND ITS APPLICATION TO MAGNETIZATION PATTERN RELAXATION

To analyze the magnetization-pattern relaxation by the nonlinear dynam ical approach, an Ising model in the time-dependent spin system (kinet ic Ising model) is extended to a space-dependent spin field. By solvin g the nonlinear diffusion equation on the spin order parameter derived by this formulation, the space-time evolution of the magnetization pa ttern can be traced. Specifically, the fifth-order Ginzburg-Landau-typ e equation in the null applied magnetic field is derived. Two kinds of nontrivial stationary solutions (lump and hole solutions) are present ed. The spatial distributions of the stationary solutions are algebrai c. Particularly, the lump solution is given as a square root of the Lo rentz distribution. From the results of the numerical experiment, it i s found that the lump solution is extremely unstable and decays very q uickly whereas the hole solution is stable and is not subjected to rel axation. An approximate lump solution for many spatial dimensions is i nvestigated as well.