THE HYDRODYNAMIC LIMIT FOR A SYSTEM WITH INTERACTIONS PRESCRIBED BY GINZBURG-LANDAU TYPE RANDOM HAMILTONIAN

As a microscopic model we consider a system of interacting continuum like spin field over R(d). Its evolution law is determined by the Ginzburg-Landau type random Hamiltonian and the total spin of the system is preserved by this evolution. We show that the spin field converges, under the hydrodynamic space-time scaling, to a deterministic limit which is a solution of a certain nonlinear diffusion equation. This equation describes the time evolution of the macroscopic field. The hydrodynamic scaling has an effect of the homogenization on the system at the same time.