Inverse percolation by removing straight semirigid rods from bilayer square lattices

Area of Science:

• Statistical Physics
• Complex Systems
• Network Science

Background:

• Percolation theory studies connectivity in random systems.
• Inverse percolation involves removing elements to study loss of connectivity.
• Bilayer lattices introduce complexities compared to single layers.

Purpose of the Study:

• Investigate inverse percolation in a bilayer square lattice by removing monomer groups (k).
• Analyze critical concentrations: jamming coverage (θ_{j,k}) and inverse percolation threshold (θ_{c,k}).
• Compare findings with related monolayer and deposition models.

Main Methods:

• Numerical simulations and finite-size scaling analysis.
• Generalized random sequential adsorption mechanism for monomer removal.
• Systematic variation of monomer group size (k) and lattice size (L).

Main Results:

• Jamming coverage (θ_{j,k}) increases with k, approaching ≈0.2701 for large k.
• Inverse percolation threshold (θ_{c,k}) decreases with k for 1 ≤ k ≤ 17.
• For k ≥ 18, all jammed states are percolating; no non-percolating phase exists.

Conclusions:

• Bilayer inverse percolation differs significantly from monolayer and deposition models.
• The system's percolation transition belongs to the universality class of standard percolation.
• Network robustness and vulnerability are key factors differentiating bilayer and monolayer systems.