Monte Carlo study of the percolating cluster for the square lattice site problem

Clusters which just span finite lattices of various sizes have been generated using a Monte Carlo method. These have been analysed to form estimates of the mean values of cyclomatic index, valence and perimeter. In addition the shortest spanning self-avoiding walk has been characterised. The ramified nature of these clusters is discussed in terms of these properties.

[1]  S. Kirkpatrick.  Percolation Phenomena in Higher Dimensions: Approach to the Mean-Field Limit , 1976 .

[2]  Heather J. Ruskin,et al.  Percolation processes in d-dimensions , 1976 .

[3]  J. Hammersley,et al.  Monte Carlo Estimates of Percolation Probabilities for Various Lattices , 1962 .

[4]  E. Stoll,et al.  Monte Carlo studies of two-dimensional percolation , 1978 .

[5]  C. Domb.  Singularities of the dilute Ising ferromagnet , 1974 .

[6]  C. Domb,et al.  Shape and size of two-dimensional percolation clusters with and without correlations , 1979 .

[7]  Peter Reynolds,et al.  Large-cell renormalisation group for the backbone problem in percolation , 1979 .

[8]  D. Stauffer.  Monte Carlo Study of Density Profile, Radius, and Perimeter for Percolation Clusters and Lattice Animals , 1978 .

[9]  D. Gaunt,et al.  Percolation processes in two dimensions. II. Critical concentrations and the mean size index , 1976 .

[10]  R. J. Harrison,et al.  Monte Carlo experiments on cluster size distribution in percolation , 1979 .

[11]  J. M. Hammersley,et al.  Critical Percolation Probabilities (Bond Problem) , 1961 .

[12]  P. Dean,et al.  Monte Carlo estimates of critical percolation probabilities , 1967, Mathematical Proceedings of the Cambridge Philosophical Society.

[13]  P. Dean.  A new Monte Carlo method for percolation problems on a lattice , 1963, Mathematical Proceedings of the Cambridge Philosophical Society.

[14]  A. Hankey.  Three properties of the infinite cluster in percolation theory , 1978 .

[15]  Estimates of critical percolation probabilities for a set of two-dimensional lattices , 1972 .

[16]  The shapes of domains occurring in the droplet model of phase transitions , 1976 .

[17]  E. Stoll,et al.  Cluster shapes in lattice gases and percolation , 1975 .