Site trimer percolation on square lattices

Area of Science:

• Statistical Physics
• Complex Systems

Background:

• Percolation theory studies the formation of connected clusters in random systems.
• Understanding how particle size affects percolation is crucial for various scientific fields.

Purpose of the Study:

• To investigate the percolation of site trimers (k=3) using analytical and simulation techniques.
• To compare analytical and numerical results for the percolation threshold and critical exponent.
• To analyze the influence of object size on percolation phenomena.

Main Methods:

• Development of an analytical model based on renormalization techniques.
• Extensive computer simulations to validate analytical findings.
• Examination of five distinct deposition possibilities for site trimers, considering shape and orientation.

Main Results:

• Analytical and numerical results for the percolation threshold (p(c)) are consistently near 0.55.
• A clear trend shows that p(c) decreases as the size of the percolating objects (k) increases.
• The critical exponent ν obtained numerically closely matches the theoretical value of 4/3.

Conclusions:

• Site trimer percolation falls within the universality class of random percolation.
• The findings support the hypothesis that larger objects lead to lower percolation thresholds.
• The study provides a robust framework for analyzing percolation phenomena with varying object complexities.