  The anisotropic XY ferromagnet has been studied by Monte Carlo simulation in
a three dimensional simple cubic lattice. The increase in critical temperature
(ferro-para transition) has been noticed with increasing the strength of
anisotropy. The effects of random fields (both with full circular symmetry and
in angular window) on the critical temperature are investigated systematically
in the anisotropic XY ferromagnet in three dimensions. Reduction in the
critical temperature of anisotropic XY ferromagnet has been observed in the
presence of random field. The compensating field (the required amount of field
which preserves the critical temperature for isotropic XY ferromagnet) has been
studied as a function of the strength of anisotropy. The compensating field was
found to depend linearly on the strength of anisotropy. We have also studied
the effects of random field confined in the angular window and observed the
reduction of the critical temperature with increase of the angular extension.
The critical behaviours are formalized by the usual finite size analysis and
the estimation of critical exponents for the susceptibility and the specific
heat. .
