Heisenberg-to-Ising crossover in a random-field model with uniaxial anisotropy

Uniaxial anisotropy causes a crossover between Ising and Heisenberg behavior in a random-field model. At random-field strengths and dimensionalities, intermediate between those which give either the Ising and Heisenberg domain states, a new ``boundary'' domain state appears. A novel criterion is also derived for domain-boundary roughening in the Heisenberg limit. The two-dimensional version of this model can be applied to ferromagnetic-antiferromagnetic sandwiches with interface randomness and leads to a prediction of an exchange anisotropy effect below a critical thickness of order the domain-wall width, and an enhancement of this effect below a second critical thickness.