Método del Máximo del Cumulante

Abstract

We present a novel method for the determination of the critical point in condensation-evaporation-like phase transitions. The method was originally developed for studying thecondensation phase transition in a monolayer of adsorbed "rigid-rod" particles (k-mers) butit can be extended to other systems. The maximum cumulant method was developed fromthe phenomenological observation that the fourth-order Binder cumulant and the isotherminflection point are produced at the same value of chemical potential. The method wassuccessfully applied to several different systems, showing great precision when compared tosystems with exact analytical solution. In addition, we present mathematical arguments inorder to show analytically that the previously mentioned relationship between the fourth orderBinder cumulant and the isotherm inflection point is satisfied by evaporation-condensationsystems under some general conditions. Numerical results from Monte Carlo simulations offour different adsorption-desorption systems (linear k-mers on square and triangular lattices,S-shaped k-mers on square lattices and k2-mers on square lattices) are presented to checkthe theoretical results and to provide evidence of the general validity and robustness of themethod.