Percolation of polyatomic species on lattice of different geometries

V.CORNETTE; A.J.RAMÍREZ-PASTOR; F.NIETO

Leuven, Belgica

Otro; International Summer School Fundamental Problems in Statistical Physics XI; 2005

The study of random percolation have been attracting a great deal of interest for many years and the activity in this field is still growing. Some aspects of the percolation process like the geometrical phase transitions occurring in the system have gained a particular impetus due to the introduction of techniques like Monte Carlo simulations and series expansions. Despite of the number of contribution to this problem, there are many aspects which are not yet completely solved. In fact, most of the studies are devoted to the percolation of molecules with single occupancy. However, if some sort of correlation exists, like particles occupying several (k) contiguous lattice sites (k-mers), the statistical problem (multisite statistics) becomes exceedingly difficult. The difficulty in the analysis of the multisite statistics is mainly associated to three factors which differentiate the k-mers statistics from the usual single particle statistics, namely: •No statistical equivalence exists between particles and vacancies. •The occupation of a given lattice site ensures that at least one of its nearest-neighbor sites is also occupied. • An isolated vacancy cannot serve to determining whether or not that site can ever become occupied. For these reasons, it has been difficult to formulate, in an analytical way, the statistics (and kinetics) of occupation for correlated particles. In this contribution we investigate the percolation of k-mers on a square lattice in the framework of a Monte Carlo (MC) analysis. We would like to present a detailed study of the finite size effects in order to discuss the universality class of the phase transition which the system undergoes. The main aim of the paper is to determine the dependence of the percolation threshold on both the size andform of the percolating k-mers and the properties of the lattice where they are deposited.