Domain growth in the two-dimensional time-dependent Ginzburg-Landau model in the presence of a random magnetic field

We present results of a numerical study of the two-dimensional time-dependent Ginzburg-Landau model with a random magnetic field. The growth of domains after a quench to low temperatures is investigated. Our results are, in general, consistent with the theories of Villain and of Grinstein and Fernandez. In particular, the predicted logarithmic growth is observed. The scaling behavior of the structure factor is also investigated. The zero-field scaling function closely agrees with the result of a theory of Ohta, Jasnow, and Kawasaki. For finite fields some evidence for the breakdown of scaling is obtained.