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

@article{Xun2021SiteAB, title={Site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in two and three dimensions.}, author={Zhipeng Xun and Dapeng Hao and Robert M. Ziff}, journal={Physical review. E}, year={2021}, volume={105 2-1}, pages={ 024105 } }

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) lattices in three dimensions, is investigated. In two dimensions, correlations between coordination number z and site thresholds p_{c} for Archimedean lattices up to 10th nearest neighbors (NN) are seen by plotting z versus 1/p_{c} and z versus -1/ln(1-p_{c}) using the data of d'Iribarne et al. [J…

## 5 Citations

### 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 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.

### Kinetics and percolation: coke in heterogeneous catalysts

- ChemistryJournal of Physics A: Mathematical and Theoretical
- 2022

In the conventional lattice percolation models, bonds or sites are open at random, whereas in reality there is often interplay of percolation and the kinetics under consideration. An interesting and…

### Catalytic Conversion of Hydrocarbons and Formation of Carbon Nanofilaments in Porous Pellets

- ChemistryCatalysis Letters
- 2022

Catalytic conversion of hydrocarbons occurring at metal nanoparticles in porous pellets is often accompanied by the formation of coke in the form of growing heterogeneous film-like aggregates or…

### 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…

## References

SHOWING 1-10 OF 69 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),…

### 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.

### 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…

### 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…

### 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…

### Equivalent-neighbor percolation models in two dimensions: Crossover between mean-field and short-range behavior

- PhysicsPhysical Review E
- 2018

We investigate the influence of the range of interactions in the two-dimensional bond percolation model, by means of Monte Carlo simulations. We locate the phase transitions for several interaction…

### Logarithmic corrections in (4+1) -dimensional directed percolation.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

There is one combination of these three observables which seems completely free of logarithmic terms and with a consistent set of fit parameters, one obtains still much improvement over the leading log approximation.

### High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials

- Mathematics
- 2014

The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. This comprises the square, triangular, hexagonal…

### Critical polynomials in the nonplanar and continuum percolation models.

- PhysicsPhysical review. E
- 2021

It is found that the critical polynomial method can be a powerful tool for studying nonplanar and continuum systems in statistical mechanics and suffers much less from finite-size corrections than other quantities.