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Site–bond percolation on triangular lattices: Monte Carlo simulation and analytical approach

Author

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  • González, M.I.
  • Centres, P.
  • Lebrecht, W.
  • Ramirez-Pastor, A.J.
  • Nieto, F.

Abstract

A generalization of the pure site and pure bond percolation problems called site–bond percolation on a triangular lattice is studied. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as S∩B and S∪B) for site–bond percolation are used. In S∩B (S∪B), two points are said to be connected if a sequence of occupied sites and (or) bonds joins them. By using finite-size scaling theory, data from S∩B and S∪B are analyzed in order to determine (i) the phase boundary between the percolating and non-percolating regions and (ii) the numerical values of the critical exponents of the phase transition occurring in the system. A theoretical approach, based on exact calculations of configurations on finite triangular cells, is applied to study the site–bond percolation on triangular lattices. The percolation processes have been monitored by following the percolation function, defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied elements. A comparison of the results obtained by these two methods has been performed and discussed.

Suggested Citation

  • González, M.I. & Centres, P. & Lebrecht, W. & Ramirez-Pastor, A.J. & Nieto, F., 2013. "Site–bond percolation on triangular lattices: Monte Carlo simulation and analytical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6330-6340.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:24:p:6330-6340
    DOI: 10.1016/j.physa.2013.09.001
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    Cited by:

    1. Huang, Xudong & Yang, Dong & Kang, Zhiqin, 2021. "Impact of pore distribution characteristics on percolation threshold based on site percolation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).

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