Site trimer percolation on square lattices

W. Lebrecht, E. E. Vogel, J. F. Valdés, A. J. Ramirez-Pastor, P. M. Centres, M. I. González, and F. D. Nieto
Phys. Rev. E 92, 012129 – Published 23 July 2015

Abstract

Percolation of site trimers (k-mers with k=3) is investigated in a detailed way making use of an analytical model based on renormalization techniques in this problem. Results are compared to those obtained here by means of extensive computer simulations. Five different deposition possibilities for site trimers are included according to shape and orientation of the depositing objects. Analytical results for the percolation threshold pc are all close to 0.55, while numerical results show a slight dispersion around this value. A comparison with pc values previously reported for monomers and dimers establishes the tendency of pc to decrease as k increases. Critical exponent ν was also obtained both by analytical and numerical methods. Results for the latter give values very close to the expected value 4/3 showing that this percolation case corresponds to the universality class of random percolation.

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  • Received 29 April 2015
  • Revised 19 June 2015

DOI:https://doi.org/10.1103/PhysRevE.92.012129

©2015 American Physical Society

Authors & Affiliations

W. Lebrecht, E. E. Vogel*, and J. F. Valdés

  • Departamento de Ciencias Físicas, Universidad de La Frontera, Casilla 54-D, Temuco, Chile

A. J. Ramirez-Pastor, P. M. Centres, M. I. González, and F. D. Nieto

  • Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Ejército de los Andes 950, D5700HHW, San Luis, Argentina

  • *To whom all correspondence should be addressed.

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Vol. 92, Iss. 1 — July 2015

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