Sublattice-selective percolation on bipartite planar lattices

Area of Science:

• Statistical Physics
• Condensed Matter Physics
• Network Science

Background:

• Conventional site percolation uses uniform site occupation probabilities.
• Bipartite lattices require distinct probabilities for each sublattice, defining sublattice-selective percolation.

Purpose of the Study:

• Determine the phase diagram for sublattice-selective percolation on 2D square and Lieb lattices.
• Investigate the universality class of sublattice-selective percolation.
• Analyze critical exponents at the percolation transition.

Main Methods:

• Adapted Newman-Ziff algorithm for phase diagram determination.
• Analysis of critical exponents at the percolation transition.
• Exact solution for sublattice-selective percolation on the Bethe lattice.

Main Results:

• The phase diagram for sublattice-selective percolation on 2D square and Lieb lattices was quantified.
• Critical exponents confirm sublattice-selective percolation belongs to the same universality class as conventional site percolation.
• Exact solution on the Bethe lattice further supports this conclusion.

Conclusions:

• Sublattice-selective percolation shares universality with conventional site percolation across different lattice types.
• The adapted Newman-Ziff algorithm effectively characterizes percolation on bipartite lattices.
• Findings contribute to understanding phase transitions in disordered systems.