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Site trimer percolation on square lattices.

W Lebrecht1, E E Vogel1, J F Valdés1

  • 1Departamento de Ciencias Físicas, Universidad de La Frontera, Casilla 54-D, Temuco, Chile.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary
This summary is machine-generated.

This study explores site trimer percolation using analytical and simulation methods. Results indicate that the percolation threshold decreases as object size increases, aligning with random percolation universality.

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Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • Percolation theory studies the formation of connected clusters in random systems.
  • Understanding how particle size affects percolation is crucial for various scientific fields.

Purpose of the Study:

  • To investigate the percolation of site trimers (k=3) using analytical and simulation techniques.
  • To compare analytical and numerical results for the percolation threshold and critical exponent.
  • To analyze the influence of object size on percolation phenomena.

Main Methods:

  • Development of an analytical model based on renormalization techniques.
  • Extensive computer simulations to validate analytical findings.
  • Examination of five distinct deposition possibilities for site trimers, considering shape and orientation.

Main Results:

  • Analytical and numerical results for the percolation threshold (p(c)) are consistently near 0.55.
  • A clear trend shows that p(c) decreases as the size of the percolating objects (k) increases.
  • The critical exponent ν obtained numerically closely matches the theoretical value of 4/3.

Conclusions:

  • Site trimer percolation falls within the universality class of random percolation.
  • The findings support the hypothesis that larger objects lead to lower percolation thresholds.
  • The study provides a robust framework for analyzing percolation phenomena with varying object complexities.