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A simple site-diluted classical XY model is proposed to study the magneticproperties of the ferromagnetic polycrystallineFe[Se$_2$CN(C$_2$H$_5$)$_2$]$_2$Cl diluted with diamagneticZn[S$_2$CN(C$_2$H$_5$)$_2$]$_2$. An extra superexchange interaction is assumedbetween next-nearest-neighbors on a simple cubic lattice, which are induced bya diluted ion. The critical properties are obtained by Monte Carlo simulationsusing a hybrid algorithm, single histograms procedures and finite-size scalingtechniques. Quite good fits to the experimental results of the orderingtemperature are obtained, namely its much less rapidly decreasing with dilutionthan predicted by the standard diluted 3$d$ XY model, and the change incurvature around $86\%$ of the magnetic Fe[Se$_2$CN(C$_2$H$_5$)$_2$]$_2$Clcompound.

Monte Carlo Simulations of the site-diluted 3d XY model with  superexchange interaction: application to Fe[Se$_2$CN(C$_2$H$_5$)$_2$]$_2$Cl  -- Zn[S$_2$CN(C$_2$H$_5$)$_2$]$_2$ diluted magnets