# Simple Cubic Random-Site Percolation Thresholds for Complex Neighbourhoods

@article{Kurzawski2011SimpleCR, title={Simple Cubic Random-Site Percolation Thresholds for Complex Neighbourhoods}, author={Lukasz Kurzawski and Krzysztof Malarz}, journal={Reports on Mathematical Physics}, year={2011}, volume={70}, pages={163-169} }

## 38 Citations

### Simple cubic random-site percolation thresholds for neighborhoods containing fourth-nearest neighbors.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

In this paper, random-site percolation thresholds for a simple cubic (SC) lattice with site neighborhoods containing next-next-next-nearest neighbors (4NN) are evaluated with Monte Carlo simulations.…

### Site percolation thresholds on triangular lattice with complex neighborhoods.

- Computer Science, PhysicsChaos
- 2020

A fast Monte Carlo algorithm is used for determining thresholds pc for random site percolation on a triangular lattice for neighborhoods containing nearest (NN), next-nearest (2NN, next-next-Nearest (3NN), and next-Next-next -next-ne nearest (4NN) neighbors, and their combinations forming regular hexagons.

### Precise bond percolation thresholds on several four-dimensional lattices

- PhysicsPhysical Review Research
- 2020

We study bond percolation on several four-dimensional (4D) lattices, including the simple (hyper) cubic (SC), the SC with combinations of nearest neighbors and second nearest neighbors (SC-NN+2NN),…

### 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.

### Bond percolation on simple cubic lattices with extended neighborhoods.

- PhysicsPhysical review. E
- 2020

The results show that the percolation thresholds of these and other three-dimensional lattices decrease monotonically with the coordination number z quite accurately according to a power-law p_{c}∼z^{-a} with exponent a=1.111.

### 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
- 2022

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…

### 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…

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