EXACT ZERO-TEMPERATURE CRITICAL-BEHAVIOR OF THE FERROMAGNET IN THE UNIAXIAL RANDOM-FIELD

The zero-temperature critical behaviours of the classical Heisenberg a nd XY ferromagnets in the uniaxial random field are studied in the arb itrary spatial dimension. Exact results are obtained for the magnetiza tion, transversal to the random field direction, at the Gaussian and b imodal distributions of the random field. For the Gaussian distributio n 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 magnetiz ation 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 a mplitude. The same critical behaviour is expected for related systems, for example random antiferromagnets in the uniform held.