Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity

TL;DR

This study uses Monte Carlo simulations to analyze phase transitions in a three-dimensional anisotropic XY ferromagnet with quenched nonmagnetic impurities, revealing how impurity concentration affects critical temperatures and exponents.

Contribution

It provides new insights into how impurities influence phase transition temperatures and critical exponents in anisotropic XY ferromagnets through detailed finite size scaling analysis.

Findings

Pseudocritical temperature decreases with impurity concentration p.

Linear dependence of T_c* on anisotropy parameter λ with p-dependent slope.

Estimated critical exponents for magnetization and susceptibility.

Abstract

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.