Maximum Cumulant Method for studying condensation-evaporation phase transitions

DOS SANTOS, GONZALO; LINARES D. H.; RAMIREZ PASTOR A.J.

Pucón

Seminario; Seminario Intensivo, ?Materia Condensada y Física Estadística? , XIV SIMAFE 2019; 2019

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 the condensation phase transition in a monolayer of adsorbed rigid-rod particles (k-mers) but it can be extended to other systems. The maximum cumulant method was developed from the phenomenological observation that the fourth-order Binder cumulant and the isotherm inflection point are produced at the same value of chemical potential. The method was successfully applied to several different systems, showing great precision when compared to systems with exact analytical solution. In addition, we present mathematical arguments in order to show analytically that the previously mentioned relationship between the fourth order Binder cumulant and the isotherm inflection point is satisfied by evaporation-condensation systems under some general conditions. Numerical results from Monte Carlo simulations of four 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 check the theoretical results and to provide evidence of the general validity and robustness of the method.