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

@article{Tran2012PercolationTO, title={Percolation thresholds on three-dimensional lattices with three nearest neighbors}, author={Jonathan Tran and Ted Yoo and Shane Stahlheber and Alex Small}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2012}, volume={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 of 4 or higher, but 3-coordinated lattices have attracted recent interest for their unusual symmetries and relevance to self-assembled materials. We have considered four lattices, with different symmetries, different underlying Bravais lattices, and different degrees of longer-range connections. As…

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## References

SHOWING 1-10 OF 34 REFERENCES

### Similarity of Percolation Thresholds on the HCP and FCC Lattices

- Physics
- 1999

Extensive Monte Carlo simulations were performed in order to determine the precise values of the critical thresholds for site (phcpc, S=0.199 255 5±0.000 001 0) and bond (phcpc, B=0.120 164 0±0.000…

### Percolation on two- and three-dimensional lattices.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

A highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff is applied to treat percolation problems to confirm the universal aspect of the wrapping probabilities regarding site and bond dilution.

### Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation

- Physics
- 1998

Extensive Monte Carlo simulations were performed to evaluate the excess number of clusters and the crossing probability function for three-dimensional percolation on the simple cubic (s.c.),…

### Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices

- Physics
- 1998

Extensive Monte-Carlo simulations were performed to study bond percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices, using an epidemic kind…

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

- Materials Science
- 1998

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…

### Universal formulas for percolation thresholds.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

A power law is postulated for both site and bond percolation thresh- olds and is found to be also valid for Ising critical temperatures.

### Fast Monte Carlo algorithm for site or bond percolation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

An efficient algorithm is described that can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system.

### Introduction To Percolation Theory

- Physics
- 1985

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in…

### Trapping thresholds in invasion percolation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

It is found that in most cases the thresholds for invasion and ordinary percolation coincide, however, for coordination numbers less than five the thresholds diverge.

### A unique 3D alternating ferro- and antiferromagnetic manganese azide system with threefold interpenetrating (10,3) nets.

- Materials ScienceAngewandte Chemie
- 2004

The designed self-assembly of azido bridging ligands with bis(monodentate) or bis(bidentate) ligands by the design of high-dimensionality transition-metal–azido coordination polymers is attractive, but it still remains a great challenge.