Site and bond percolation in linearly distorted triangular and square lattices

Area of Science:

• Statistical physics
• Complex systems
• Network science

Background:

• Percolation theory studies connectivity in random systems.
• Lattice distortions can alter connectivity and critical phenomena.
• Previous studies focused on geometry-preserving distortions.

Purpose of the Study:

• Investigate site and bond percolation under linear lattice distortion.
• Analyze the impact of distortion parameter and connection threshold on percolation thresholds.
• Compare behavior in triangular and square lattices.

Main Methods:

• Extensive Monte Carlo simulations.
• Finite-size scaling analyses.
• Analysis of site and bond percolation thresholds under linear distortion.

Main Results:

• Triangular lattices exhibit directional dependence in percolation thresholds due to anisotropic modifications.
• Square lattices remain isotropic, showing consistent percolation thresholds regardless of distortion direction.
• Bond percolation in triangular lattices shows complex behavior beyond average coordination number changes.

Conclusions:

• Linear distortion significantly impacts percolation thresholds, especially in anisotropic lattices like triangular ones.
• Square lattices offer a more isotropic response to linear distortion.
• The study provides insights into how lattice geometry modifications influence critical phenomena in disordered systems.