Exclusion statistics and thermodynamics of a straight k-mers lattice-gas: Analytical approximation and Monte Carlo simulations

Thermodynamics of straight k-mers gas on the square lattice is addressed from its relation to state exclusion statistics through a new analytical approximation along with a detailed MC analysis. Multiple state exclusion arising as consequence of the spatial correlation between particle states is described through exclusion spectrum functions and related to the thermodynamic potentials. An effective lattice analytical approximation is introduced through configurational mapping and applied to dimers (k=2) and trimers (k=3). Simple closed analytical forms for the coverage dependence of multiple state exclusion probabilities and chemical potential are obtained. Remarkable agreement with fast relaxation MC simulations carried out in this work is already found for the lowest degree of approximation.