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The anisotropic XY ferromagnet has been studied by Monte Carlo simulation ina three dimensional simple cubic lattice. The increase in critical temperature(ferro-para transition) has been noticed with increasing the strength ofanisotropy. The effects of random fields (both with full circular symmetry andin angular window) on the critical temperature are investigated systematicallyin the anisotropic XY ferromagnet in three dimensions. Reduction in thecritical temperature of anisotropic XY ferromagnet has been observed in thepresence of random field. The compensating field (the required amount of fieldwhich preserves the critical temperature for isotropic XY ferromagnet) has beenstudied as a function of the strength of anisotropy. The compensating field wasfound to depend linearly on the strength of anisotropy. We have also studiedthe effects of random field confined in the angular window and observed thereduction of the critical temperature with increase of the angular extension.The critical behaviours are formalized by the usual finite size analysis andthe estimation of critical exponents for the susceptibility and the specificheat. .

Critical behaviours of anisotropic XY ferromagnet in the presence of random field