# Site percolation thresholds on triangular lattice with complex neighborhoods.

@article{Malarz2020SitePT, title={Site percolation thresholds on triangular lattice with complex neighborhoods.}, author={Krzysztof Malarz}, journal={Chaos}, year={2020}, volume={30 12}, pages={ 123123 } }

We determine thresholds pc for random site percolation on a triangular lattice for neighborhoods containing nearest (NN), next-nearest (2NN), next-next-nearest (3NN), next-next-next-nearest (4NN), and next-next-next-next-nearest (5NN) neighbors, and their combinations forming regular hexagons (3NN+2NN+NN, 5NN+4NN+NN, 5NN+4NN+3NN+2NN, and 5NN+4NN+3NN+2NN+NN). We use a fast Monte Carlo algorithm, by Newman and Ziff [Phys. Rev. E 64, 016706 (2001)], for obtaining the dependence of the largest…

## 6 Citations

### Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit.

- PhysicsPhysical review. E
- 2021

By means of extensive Monte Carlo simulation, extended-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors up to the eighth nearest neighbors for the square lattice and the ninth nearestNeighborhoods are found using a single-cluster growth algorithm.

### Percolation thresholds on a triangular lattice for neighborhoods containing sites up to the fifth coordination zone.

- PhysicsPhysical review. E
- 2021

We determine thresholds p_{c} for random-site percolation on a triangular lattice for all available neighborhoods containing sites from the first to the fifth coordination zones, including their…

### Random site percolation on honeycomb lattices with complex neighborhoods.

- PhysicsChaos
- 2022

We present a rough estimation-up to four significant digits, based on the scaling hypothesis and the probability of belonging to the largest cluster vs the occupation probability-of the critical…

### Site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in two and three dimensions.

- PhysicsPhysical review. E
- 2022

Extended-range percolation on various regular lattices, including all 11 Archimedean lattices in two dimensions and the simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc)…

### Site and bond percolation on four-dimensional simple hypercubic lattices with extended neighborhoods

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
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The asymptotic behavior of the percolation threshold p c and its dependence upon coordination number z is investigated for both site and bond percolation on four-dimensional lattices with compact…

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