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Cluster diversity and entropy on the percolation model: the lattice animal identification algorithm
1VisionLab-Department of Physics, University of Antwerp-RUCA, Groenenborgerlaan 171, Antwerp B-2020, Belgium.
Summary
A new algorithm identifies lattice animals by shape, not size, advancing percolation theory. This method reveals critical probabilities linked to the percolation transition and system complexity.
Area of Science:
- Statistical Physics
- Computational Physics
- Complex Systems
Background:
- The site-percolation model is fundamental in statistical physics for studying connectivity.
- Existing algorithms like Hoshen-Kopelman classify clusters by size, limiting shape-based analysis.
- Understanding lattice animal shapes is crucial for characterizing complex systems.
Purpose of the Study:
- To develop a novel algorithm for identifying and counting lattice animals based on their distinct shapes.
- To differentiate between fixed and free lattice animals.
- To analyze cluster diversity and entropy in percolation systems.
Main Methods:
- Developed a shape-coding algorithm for lattice animals using nearest-neighbor information.
- Adapted the enhanced Hoshen-Kopelman algorithm to generate nearest-neighbor code sequences.
- Employed Monte Carlo simulations on large planar square lattices (up to 2000x2000).
Main Results:
- Successfully represented lattice animals by unique code sequences.
- Calculated system cluster diversity and cluster entropy.
- Determined critical probabilities associated with the maxima of these functions.
Conclusions:
- The new algorithm provides a shape-based classification of clusters, complementing size-based methods.
- The identified critical probabilities are directly linked to the percolation transition.
- The findings offer insights into the complexity of percolation systems through cluster shape analysis.