Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity

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.