Theoretical study of disordered $Fe$-$Ru$ alloys: a Monte Carlo approach

We study the magnetic properties and critical behaviour of quenched $F\lowercase{e}_{1-\lowercase{x}}R\lowercase{u}_{\lowercase{x}}$ alloys on a bcc lattice, for the following ruthenium concentrations: $x=0\%$, $4\%$, $6\%$ and $8\%$. This study is carried out within a Monte Carlo approach employing multiple histogram reweighting to analyse the data generated in the simulations. By means of a finite-size scaling analysis of several themodynamic quantities, taking into account up to the leading irrelevant scaling field term, we find estimates of the critical exponents $\alpha$, $\beta$, $\gamma$ and $\nu$ and critical temperature of our model. Our results for $x=0\%$ are in excelent agreement with those for the three-dimensional pure Ising model in the literature, as expected. We show that our estimates of critical exponents for $x=4\%$, $6\%$ and $8\%$ are consistent with those reported for the transition line between paramagnetic and ferromagnetic phases of both randomly dilute and $\pm J$ Ising models. We also compare our results for the behaviour of the Curie temperature as a function of ruthenium concentration and magnetization as a function of temperature with experimental and mean-field results reported elsewhere.