Domain size in the presence of random fields

We consider the size of domains formed in ordered systems in the presence of quenched random fields. We argue that below the critical dimension, the domain size shows a nonmonotonic dependence on the correlation length of the random field. If the random field is slowly varying in space, the order parameter follows the field, and the domain size is comparable to the correlation length. If the field is rapidly varying, the domain size becomes larger than the correlation length, and diverges as the correlation length of the random field goes to zero.