Critical behaviours of anisotropic and impure XY ferromagnets

Olivia Mallick, Muktish Acharyya

Published 2022-08-22Version 1

The three-dimensional anisotropic XY ferromagnet has been investigated by extensive Monte Carlo simulation using the Metropolis single spin flip algorithm. The magnetisation ($M$) and the susceptibility ($\chi$) are measured and studied as functions of the temperature of the system. For uniform (over space) anisotropy the ferro-para phase transition has been found to occur for a higher temperature than that compared to the isotropic case. The system gets ordered at higher temperatures for higher values of the strength of anisotropy. The contrasting behaviour is observed in the case of distributed (over space) anisotropy. For all three different kinds of the distribution (random uniform, Gaussian, and bimodal) of anisotropy, the system gets ordered in the lower temperatures for higher values of the width of the distribution of anisotropy. We have provided the comprehensive phase boundaries in the case of distributed anisotropy. We have also studied the critical behaviour of isotropic impure (diluted by non-magnetic impurity) XY ferromagnet. Here, the pseudo-critical temperature was found to shift to the lower temperature for higher values of the concentration of impurity. The critical exponents for the scaling laws $M \sim L^{-{\beta\over\nu}}$ and $\chi \sim L^{{\gamma}\over{\nu}}$ are estimated in the finite size analysis to determine the universality class of such anisotropic and impure XY ferromagnets.