Related Experiment Videos
Percolation threshold of correlated two-dimensional lattices
1Physics Department, Marquette University, Milwaukee, Wisconsin 53233, USA.
Summary
This study extends percolation simulations to various 2D lattices, finding results largely independent of lattice size. Percolation thresholds on specific lattices satisfy the Sykes-Essam relation, offering insights into correlated percolation phenomena.
Area of Science:
- Statistical Physics
- Condensed Matter Physics
- Computational Physics
Background:
- Percolation theory studies the formation of connected clusters in random systems.
- Previous work simulated percolation on correlated square and cubic lattices.
- Understanding percolation on diverse lattices is crucial for various scientific fields.
Purpose of the Study:
- To extend percolation simulations to a wider range of common two-dimensional lattices.
- To investigate the size dependence of percolation thresholds on these lattices.
- To examine the validity of theoretical relations for percolation thresholds.
Main Methods:
- Simulations were performed on triangular, square 1-2, honeycomb, and kagome lattices.
- Lattice sizes up to 1024x1024 sites were utilized.
- Results were analyzed for size independence and fitted to Gaussian functions.
Main Results:
- Percolation simulation results showed independence from lattice size, except possibly at large correlation lengths.
- A Gaussian function fit was applied to the correlation length, though theoretical significance is debated.
- For specific matching lattices, percolation thresholds adhered to the Sykes-Essam relation.
Conclusions:
- The study successfully extended percolation simulations to diverse 2D lattices.
- Results suggest a general independence of percolation thresholds from lattice size.
- The Sykes-Essam relation holds for certain lattice configurations, validating theoretical predictions.