# Bond percolation on simple cubic lattices with extended neighborhoods.

@article{Xun2020BondPO, title={Bond percolation on simple cubic lattices with extended neighborhoods.}, author={Zhipeng Xun and Robert M. Ziff}, journal={Physical review. E}, year={2020}, volume={102 1-1}, pages={ 012102 } }

We study bond percolation on the simple cubic lattice with various combinations of first, second, third, and fourth nearest neighbors by Monte Carlo simulation. Using a single-cluster growth algorithm, we find precise values of the bond thresholds. Correlations between percolation thresholds and lattice properties are discussed, and our results show that the percolation thresholds of these and other three-dimensional lattices decrease monotonically with the coordination number z quite…

## 8 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.

### 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),…

### Relay charge transport in thunderclouds and its role in lightning initiation

- PhysicsScientific reports
- 2022

A new mechanism of charge transport inside a thundercloud is suggested and numerically investigated. The considered mechanism can be called “relay” because it is provided by a dynamical network of a…

### Percolation in a simple cubic lattice with distortion.

- Computer SciencePhysical review. E
- 2022

The values of the relevant critical exponents of the transition strongly indicate that percolation in regular and distorted simple cubic lattices belong to the same universality class.

### Cumulative Merging Percolation: A long-range percolation process in networks

- Medicine, Computer SciencePhysical review. E
- 2022

Percolation on networks is a common framework to model a wide range of processes, from cascading failures to epidemic spreading. Standard percolation assumes short-range interactions, implying that…

### 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…

## References

SHOWING 1-10 OF 75 REFERENCES

### 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),…

### Percolation transitions in two dimensions.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

The amplitude of the power-law correction associated with X_{t2}=4 is found to be dependent on the orientation of the lattice with respect to the cylindrical geometry of the finite systems.

### Simultaneous analysis of three-dimensional percolation models

- Physics, Mathematics
- 2013

We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice…

### Site percolation and random walks on d-dimensional Kagomé lattices

- Mathematics
- 1998

The site percolation problem is studied on d-dimensional generalizations of the Kagome lattice. These lattices are isotropic and have the same coordination number q as the hyper-cubic lattices in d…

### Exact bond percolation thresholds in two dimensions

- Mathematics
- 2006

Recent work in percolation has led to exact solutions for the site and bond critical thresholds of many new lattices. Here we show how these results can be extended to other classes of graphs,…

### Bond and site percolation in three dimensions.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

The bond and site percolation models are simulated on a simple-cubic lattice with linear sizes up to L=512, and various universal amplitudes are obtained, including wrapping probabilities, ratios associated with the cluster-size distribution, and the excess cluster number.

### Bond percolation thresholds on Archimedean lattices from critical polynomial roots

- PhysicsPhysical Review Research
- 2020

We present percolation thresholds calculated numerically with the eigenvalue formulation of the method of critical polynomials; developed in the last few years, it has already proven to be orders of…

### Series expansion of the percolation threshold on hypercubic lattices

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2018

We study proper lattice animals for bond- and site-percolation on the hypercubic lattice to derive asymptotic series of the percolation threshold pc in 1/d, The first few terms of these series were…

### Exact site percolation thresholds using a site-to-bond transformation and the star-triangle transformation.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

A correlated bond problem on the hexagonal lattice is solved by use of the star-triangle transformation and the site problem is solved, by a particular choice of correlations derived from a site-to-bond transformation, on the martini lattice.

### Square-lattice site percolation at increasing ranges of neighbor bonds.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

The existing Galam-Mauger universal formula for percolation thresholds does not reproduce the data showing dimension and coordination number are not sufficient to build a universal law which extends to complex lattices.