# Calculation of Percolation Thresholds in High Dimensions for FCC, BCC and Diamond Lattices

@article{Marck1998CalculationOP, title={Calculation of Percolation Thresholds in High Dimensions for FCC, BCC and Diamond Lattices}, author={Steven van der Marck}, journal={International Journal of Modern Physics C}, year={1998}, volume={09}, pages={529-540} }

Site and bond percolation thresholds are calculated for the face centered cubic, body centered cubic and diamond lattices in four, five and six dimensions. The results are used to study the behavior of percolation thresholds as a functions of dimension. It is shown that the predictions from a recently proposed invariant for percolation thresholds are not satisfactory for these lattices.

## 22 Citations

### An Investigation of Site-Bond Percolation on Many Lattices

- Computer Science
- 1999

It is shown here that there are strong deviations from the known approximate equations in the line of threshold values, and an alternative parametrization is proposed that lies much closer to the numerical values.

### Percolation threshold of a simple cubic lattice with fourth neighbors: the theory and numerical calculation with parallelization

- Physics
- 2013

The method of nding a percolation threshold xc of innite lattice in the problem of nodes is proposed. Theoretically was shown that curves of conditional probability of percolation of nite lattices…

### 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…

### Simultaneous analysis of three-dimensional percolation models

- Physics, MathematicsFrontiers of Physics
- 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…

### 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.

### Percolation thresholds on three-dimensional lattices with three nearest neighbors

- Physics
- 2013

We present a study of site and bond percolation on periodic lattices with three nearest neighbors per site. Essentially all previous studies of percolation in 3D have considered coordination numbers…

### 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…

### Site percolation on lattices with low average coordination numbers

- Physics
- 2014

We present a study of site and bond percolation on periodic lattices with (on average) fewer than three nearest neighbors per site. We have studied this issue in two contexts: by simulating oxides…

### 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),…

### Beyond the percolation universality class: the vertex split model for tetravalent lattices

- Physics
- 2015

We propose a statistical model defined on tetravalent three-dimensional lattices in general and the three-dimensional diamond network in particular where the splitting of randomly selected nodes…

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