Abstract
The lattice approximation to a time-dependent Ginzburg-Landau equation is investigated in the presence of a small external field. The evolution law conserves the spin, but is not reversible. A nonlinear diffusion equation of divergence type is obtained in the hydrodynamic limit. The proof extends to certain stochastically perturbed Hamiltonian systems.
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Fritz, J., Maes, C. Derivation of a hydrodynamic equation for Ginzburg-Landau models in an external field. J Stat Phys 53, 1179–1206 (1988). https://doi.org/10.1007/BF01023863
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DOI: https://doi.org/10.1007/BF01023863