Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity

The equilibrium behaviors of the anisotropic XY ferromagnet, with nonmagnetic impurity, have been investigated in three dimensions by Monte Carlo simulation using Metropolis algorithm. Two different types of anisotropy, namely, the bilinear exchange type and single-site anisotropy are considered here. The thermodynamic behaviors of the components of the magnetizations (M), susceptibility (χ) and the specific heat (C) have been studied systematically through extensive Monte Carlo simulations. The ferro–para phase transition has been observed to take place at a lower temperature for impure anisotropic XY ferromagnet. The pseudocritical temperature (Tc∗) 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 (λ), the pseudocritical temperature (Tc∗) increases linearly with λ 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 (Tc∗) 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 (UL) for different system sizes (L). The critical magnetization (M(Tc)) and the maximum value of the susceptibility (χp) are calculated for different system sizes (L). The critical exponents for the assumed scaling laws, M(Tc)∼L−βν and χp∼Lγν, are estimated through the finite size analysis. We have estimated, βν, equals 0.48±0.05 and 0.37±0.04 for bilinear exchange and single-site anisotropy, respectively. We have also estimated, γν equals 1.78±0.05 and 1.81±0.05 for bilinear exchange and single-site anisotropy, respectively.