Exact zero-temperature critical behaviour of the ferromagnet in the uniaxial random field

The zero-temperature critical behaviours of the classical Heisenberg and XY ferromagnets in the uniaxial random field are studied in the arbitrary spatial dimension. Exact results are obtained for the magnetization, transversal to the random field direction, at the Gaussian and bimodal distributions of the random field. For the Gaussian distribution the critical behaviour in strong random fields is independent of the spatial dimension. The transversal magnetization, m(perpendicular to) similar to Inh(0)/h(0)(2), where h(0) is the distribution width. For the bimodal distribution of the random field, the transversal magnetization obeys the law m(perpendicular to) similar to exp(-constant/(H-c - H)(D/2)), where H-c is a critical field, and H is the random field amplitude. The same critical behaviour is expected for related systems, for example random antiferromagnets in the uniform held.