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Percolation in a simple cubic lattice with distortion.
Sayantan Mitra1, Dipa Saha1, Ankur Sensharma1
1Department of Physics, University of Gour Banga, Malda - 732103, West Bengal, India.
Physical Review. E
|October 21, 2022
Summary
This study numerically investigates site percolation in distorted simple cubic lattices. Results show how lattice distortion and connection thresholds influence percolation thresholds, revealing distinct behaviors based on distortion levels.
Area of Science:
- Statistical Physics
- Condensed Matter Physics
- Computational Physics
Background:
- Percolation theory studies the connectivity of random systems.
- Simple cubic lattices are fundamental models in physics.
- Lattice distortions can alter system properties.
Purpose of the Study:
- To numerically characterize site percolation in a distorted simple cubic lattice.
- To investigate the impact of lattice distortion and connection thresholds on percolation.
- To compare the distorted lattice model with existing percolation models.
Main Methods:
- Numerical simulations using the Newman-Ziff algorithm.
- Systematic and random dislocation of lattice sites.
- Tunable distortion parameter and connection threshold.
Main Results:
- Percolation threshold increases with distortion for connection thresholds >= lattice constant.
- Percolation threshold shows a decrease-then-increase trend for connection thresholds < lattice constant.
- Variations explained by changes in occupied bond fraction; critical exponents indicate same universality class as regular lattices.
Conclusions:
- The model exhibits distinct behavior compared to site-bond percolation.
- Lattice distortion significantly impacts percolation thresholds in a tunable manner.
- Percolation in distorted lattices shares universality with regular lattices.
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