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Bond percolation in distorted square and triangular lattices.

Bishnu Bhowmik1, Sayantan Mitra2, Robert M Ziff3

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Summary
This summary is machine-generated.

Bond percolation in distorted lattices shows complex behavior. The bond percolation threshold increases with distortion for square and triangular lattices when the connection threshold exceeds lattice constant 1.

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Area of Science:

  • Statistical physics
  • Condensed matter physics
  • Network science

Background:

  • Percolation theory studies connectivity in random systems.
  • Lattice distortions can significantly alter network properties.
  • Understanding bond percolation is crucial for materials science and network analysis.

Purpose of the Study:

  • Investigate bond percolation in distorted square and triangular lattices.
  • Analyze the impact of site dislocations and connection thresholds on percolation thresholds.
  • Characterize the critical connection threshold for spanning configurations.

Main Methods:

  • Monte Carlo simulations were employed.
  • Lattices were distorted by random site dislocations, controlled by parameter α.
  • Bond occupation was determined by bond length (δ) and connection threshold (d).

Main Results:

  • For d > 1, bond percolation threshold (p_b) increases with distortion (α) for both lattices.
  • Square lattices show no spanning for d ≤ 1, while triangular lattices do, with p_b decreasing at low α.
  • A critical connection threshold (d_c) was identified, below which no spanning occurs, exhibiting distinct behaviors for square and triangular lattices.

Conclusions:

  • Lattice geometry and distortion significantly influence bond percolation thresholds.
  • The average coordination number correlates with observed percolation behavior.
  • The critical connection threshold (d_c) provides a fundamental parameter for lattice connectivity analysis.