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Critical temperature determination on a square-well fluid using an adaptation of the Microcanonical-ensemble computer simulation method

In this work a novel method to evaluate the liquid-vapor critical temperature using a generalization of the Microcanonical-ensemble computer simulation method (MCE) is presented. The isotherms of the chemical potential versus densities are obtained for a square-well (SW) fluid with interaction range $λ/σ= 1.5$: From these curves it can be extracted the critical temperature for different system sizes observing the change of the slope from the chemical potential's curve in the critical region as function of the temperature. Working with different systems sizes and Finite Size Scaling (FSS) Theory the critical temperature $T_c=1.2180(29)$ and the critical exponent $ν=0.65(3)$ are obtained, without previous knowledge of $T_c$ or $ν$. These results are in good agreement with the reported values for this system.