Open Conference Systems, StatPhys 27 Main Conference

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Percolation of aligned rigid rods on square and triangular lattices
Pablo Longone, Paulo Marcelo Centres, Antonio J Ramirez-Pastor

##manager.scheduler.building##: Edificio Santa Maria
##manager.scheduler.room##: Auditorio San Agustin
Date: 2019-07-08 11:45 AM – 03:30 PM
Last modified: 2019-06-15

Abstract


The percolation behavior of aligned rigid rods of length k (k-mers) on square and triangular lattices hasbeen studied by numerical simulations and finite-size scaling analysis. The k-mers, containing k identical units(each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The connectivity analysis was carried out by following the probability RL,k(p) that a lattice composed of L × L sites percolates at a concentration p of sites occupied by particles of size k. The dependence of the percolation threshold pc(k) as a function of k was determined. In the case of square lattices, pc(k) exhibits a decreasing function when it is plotted as a function of the k-mer size. This behavior is completely different to that observed for triangular lattices, where the percolation threshold increases with k. The present result clearly demonstrates that the structure of the lattice plays a fundamental role in determining the statistics and percolation properties of extended objects. In addition, the effect of the anisotropy on the properties of the percolating phase was investigated. The results revealed that, (1) the intersection points of the curvesof RL,k(p) for different system sizes exhibit nonuniversal critical behavior, varying continuously with changesin the k-mer size. This behavior is completely different to that observed for the isotropic case, where the crossingpoint of the curves of RL,k(p) do not modify their numerical value as k is increased; and (2) while for finite systems the anisotropy of the deposited layer favors the percolation along the parallel direction to the nematic axis, in the thermodynamic limit, the value of the percolation threshold is the same in both parallel and transversal directions. Finally, an exhaustive study of critical exponents and universality was carried out, showing that the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of k considered.