Monte Carlo study of the phase transitions in the classical XY ferromagnets with random anisotropy

TL;DR

This study uses Monte Carlo simulations to analyze phase transitions in three-dimensional XY ferromagnets with both constant and random anisotropy, revealing how anisotropy affects ordering temperatures and critical behavior.

Contribution

It provides a detailed Monte Carlo analysis of phase boundaries and critical exponents in XY ferromagnets with various types of random anisotropy distributions.

Findings

Higher anisotropy increases ordering temperature in constant anisotropy case.

Random anisotropy lowers the ordering temperature as distribution width increases.

Phase boundaries and critical exponents are systematically estimated.

Abstract

The three-dimensional anisotropic classical XY ferromagnet has been investigated by extensive Monte Carlo simulation using the Metropolis single spin flip algorithm. The magnetization ($M$) and the susceptibility ($\chi$) are measured and studied as functions of the temperature of the system. For constant anisotropy, the ferro-para phase transition has been found to take place at a higher temperature than that observed in the isotropic case. The system gets ordered at higher temperatures for higher values of the strength of anisotropy. The opposite scenario is observed in the case of random anisotropy. For all three different kinds of statistical distributions (uniform, Gaussian, and bimodal) of random anisotropy, the system gets ordered at lower temperatures for higher values of the width of the distribution of anisotropy. We have provided the phase boundaries in the case of random anisotropy. The critical exponents for the scaling laws $M \sim L^{-{{\beta} \over {\nu}}}$ and $\chi \sim L^{{{\gamma} \over {\nu}}} $ are estimated through the finite size analysis.