Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions

2012/05/31 by D. A. Matoz-Fernandez, D. H. Linares, A. J. Ramirez-Pastor · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Directed percolation #Nonlinear Dynamics and Pattern Formation #Percolation critical exponents #Percolation threshold #Renormalization group #Rod #Scaling #Square lattice #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #physics.chem-ph #physics.comp-ph

paper · pdf · doi:10.1140/epjb/e2012-30389-2

21 pages, 4 figures

arxiv created 2012/05/31 · openalex publication_date 2012/09/01 · arxiv updated 2015/06/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Numerical simulations and finite-size scaling analysis have been carried out to study the percolation behavior of straight rigid rods of length k (k-mers) on two-dimensional square lattices. The k-mers, containing k identical units (each one occupying a lattice site), were adsorbed at equilibrium on the lattice. The process was monitored by following the probability R_L,k(θ) that a lattice composed of L × L sites percolates at a concentration θ of sites occupied by particles of size k. A nonmonotonic size dependence was observed for the percolation threshold, which decreases for small particles sizes, goes through a minimum, and finally asymptotically converges towards a definite value for large segments. This striking behavior has been interpreted as a consequence of the isotropic-nematic phase transition occurring in the system for large values of k. Finally, the universality class of the model was found to be the same as for the random percolation model.

Citations

• Isotropic to Nematic Liquid Crystalline Phase Transition ofF-Actin Varies from Continuous to First Order
• The critical Binder cumulant for isotropic Ising models on square and triangular lattices
• Efficient Monte Carlo Algorithm and High-Precision Results for Percolation
• Pseudo-random-number generators and the square site percolation threshold
• Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations
• Percolation
• Percolation

Cited by

• Diffusion-driven self-assembly of rodlike particles: Monte Carlo simulation on a square lattice
• Vertical drying of a suspension of sticks: Monte Carlo simulation for continuous two-dimensional problem

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