# Fast Monte Carlo algorithm for site or bond percolation.

@article{Newman2001FastMC, title={Fast Monte Carlo algorithm for site or bond percolation.}, author={Mark E. J. Newman and Robert M. Ziff}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2001}, volume={64 1 Pt 2}, pages={ 016706 } }

We describe in detail an efficient algorithm for studying site or bond percolation on any lattice. The algorithm 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. We demonstrate our algorithm by using it to investigate a number of issues in percolation theory, including the position of the percolation transition for site percolation on the…

## 374 Citations

### Percolation thresholds for discrete-continuous models with nonuniform probabilities of bond formation.

- Computer SciencePhysical review. E
- 2016

A class of discrete-continuous percolation models and an efficient Monte Carlo algorithm for computing their properties are introduced and it is found that it compares favorably to well-known algorithms for simpler systems.

### 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.

### Percolation of the site random-cluster model by Monte Carlo method.

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

A site random-cluster model is proposed by introducing an additional cluster weight in the partition function of the traditional site percolation by combining the color-assignation and the Swendsen-Wang methods to design a highly efficient cluster algorithm with a small critical slowing-down phenomenon.

### Convergence of threshold estimates for two-dimensional percolation.

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

This work shows that the convergence of the average-probability estimate is described by a nontrivial correction-to-scaling exponent as predicted previously, and measures the value of this exponent to be 0.90+/-0.02.

### Dimer site-bond percolation on a triangular lattice

- Mathematics
- 2017

A generalization of the site-percolation problem, in which pairs of neighbor sites (site dimers) and bonds are independently and randomly occupied on a triangular lattice, has been studied by means…

### Site-bond percolation on simple cubic lattices: numerical simulation and analytical approach

- Physics
- 2016

The site-percolation problem on simple cubic lattices has been studied by means of numerical simulation and analytical calculations based on exact counting of configurations on finite cells.…

### 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…

### Computational studies of bond-site percolation.

- Mathematics
- 2007

Percolation theory enters in various areas of research including critical phenomena and phase transitions. Bond-site percolation is a generalization of pure percolation motivated by the fact that…

### 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.

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