  We study random-field xy spin model at T=0 numerically on lattices of up to
1000 x 1000 x 1000 spins with the accent on the weak random field. Our
numerical method is physically equivalent to slow cooling in which the system
is gradually losing the energy and relaxing to an energy minimum. The system
shows glass properties, the resulting spin states depending strongly on the
initial conditions. Random initial condition for the spins leads to the vortex
glass (VG) state with short-range spin-spin correlations defined by the average
distance between vortex lines. Collinear and some other vortex-free initial
conditions result in the vortex-free ferromagnetic (F) states that have a lower
energy. The energy difference between the F and VG states correlates with
vorticity of the VG state. Correlation functions in the F states agree with the
Larkin-Imry-Ma theory at short distances. Hysteresis curves for weak random
field are dominated by topologically stable spin walls raptured by vortex
loops. We find no relaxation paths from the F, VG, or any other states to the
hypothetical vortex-free state with zero magnetization.
