  The three dimensional anisotropic XY ferromagnet has been studied by Monte
Carlo simulation. The ferro-para phase transition has been observed to take
place at a lower temperature for impure anisotropic XY ferromagnet. The
pseudocritical temperature ($T_c^*$) has been found to decrease as the system
gets more and more impure (impurity concentration $p$ increases). In the case
of bilinear exchange type of anisotropy ($\lambda$), the pseudocritical
temperature ($T_c^*$) increases linearly with $\lambda$ for any given
concentration of nonmagnetic impurity ($p$). The slope of this linear function
has been found to depend on the impurity concentration ($p$). The slope
decreases linearly with the impurity concentration ($p$). In the case of the
single site anisotropy ($D$), the pseudocritical temperature ($T_c^*$) has been
found to decrease linearly with $p$ for fixed $D$. The critical temperature
(for a fixed set of parameter values) has been estimated from the temperature
variation of fourth order Binder cumulants ($U_L$) for different system sizes
($L$). The critical magnetisation ($M(T_c)$) and the maximum value of the
susceptibility ($\chi_p$) are calculated for different system sizes ($L$). The
critical exponents for the assumed scaling laws, $M(T_c) \sim L^{-{{\beta}
\over {\nu}}}$ and $\chi_p \sim L^{{{\gamma} \over {\nu}}}$, are estimated
through the finite size analysis. We have estimated, ${{\beta} \over {\nu}}$,
equals to $0.48\pm0.05$ and $0.37\pm0.04$ for bilinear exchange and single site
anisotropy respectively. We have also estimated, ${{\gamma} \over {\nu}}$
equals to $1.78\pm0.05$ and $1.81\pm0.05$ for bilinear exchange and single site
anisotropy respectively.
