Generation of percolation cluster perimeters by a random walk

@article{Ziff1984GenerationOP,
  title={Generation of percolation cluster perimeters by a random walk},
  author={Robert M. Ziff and Peter T. Cummings and G. Stells},
  journal={Journal of Physics A},
  year={1984},
  volume={17},
  pages={3009-3017}
}
A type of self-avoiding random walk whish generates the perimeter of two- dimensional lattice-percolation clusters is given. The algorithm has been simulated on a computer, yielding the mean perimeter length as a function of occupation probability. 

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References

SHOWING 1-10 OF 35 REFERENCES

Percolation on a randomly expanded lattice: a model of polymer gels

The authors discuss a random expansion of a lattice in which a series of 2-valent vertices are inserted between the original vertices of the lattice. The critical exponents do not change under this

Simulations of a stochastic model for cluster growth on a square lattice

An irreversible stochastic model for the growth of clusters on a square lattice is formulated and studied by Monte Carlo simulation. The growth rate has a nonlinear nonlocal dependence on the density

The ramification of large clusters near percolation threshold

A general upper bound to the perimeter polynomial is demonstrated for the site percolation problem and it is concluded that at percolation threshold p=pc the limiting mean perimeter-to-size ratio of

Diffusion-limited aggregation, a kinetic critical phenomenon

A model for random aggregates is studied by computer simulation. The model is applicable to a metal-particle aggregation process whose correlations have been measured previously. Density correlations

Scaling form for percolation cluster sizes and perimeters

Randomly generated clusters of sites on the triangular lattice at and just below pc, and clusters previously generated on the square lattice are analysed to determine their scaling form. The scaling

Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions

An exact method for determining the critical percolation probability, pc, for a number of two‐dimensional site and bond problems is described. For the site problem on the plane triangular lattice pc

Cluster shapes in lattice gases and percolation

An analysis is undertaken of the mean surface s of clusters of size n from Monte Carlo data simulating a two-dimensional Ising model. At sufficiently high temperatures the data represent a

Excluded volume effects for branched polymers: Monte Carlo results

As a simple model of randomly branched polymers, we consider the different ways that N‐bond trees may be self‐avoidingly embedded on a lattice. A general Monte Carlo approach is developed and

Thermally driven phase transitions near the percolation threshold in two dimensions

It is shown that thermally driven magnetic critical phenomena just above and just below the percolation limit can be usefully analysed using scaling theory, a further assumption concerning cluster