Percolation processes in two dimensions. I. Low-density series expansions

The derivation of low-density series expansions for the mean cluster size in random site and bond mixtures on a two-dimensional lattice is described briefly. New data are given for the triangular, simple quadratic and honeycomb lattices.

[1]  D. S. Gaunt,et al.  Derivation of low-temperature expansions for Ising model. VII. The honeycomb-triangular code system , 1975 .

[2]  D. Gaunt,et al.  Percolation processes in two dimensions IV. Percolation probability , 1976 .

[3]  B. Heap.  The Critical Temperature of Dilute Ferromagnets , 1963 .

[4]  Scott Kirkpatrick,et al.  An introduction to percolation theory , 1971 .

[5]  J. W. Essam,et al.  Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions , 1964 .

[6]  D. S. Gaunt,et al.  Derivation of low-temperature expansions for Ising model VIII. Ferromagnetic and antiferromagnetic polynomials for the honeycomb-triangular system , 1975 .

[7]  J. W. Essam,et al.  Some Cluster Size and Percolation Problems , 1961 .

[8]  C. Domb.  Fluctuation Phenomena and Stochastic Processes , 1959, Nature.

[9]  J. W. Essam,et al.  Derivation of low‐temperature expansions for Ising model. II. General theory , 1973 .

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

[11]  D. S. Gaunt,et al.  Derivation of low-temperature expansions for Ising model. V. Three-dimensional lattices-field grouping , 1973 .

[12]  J. Essam,et al.  A note on the convergence of the series expansion for the mean cluster size in random mixtures , 1973 .

[13]  D. Gaunt,et al.  Derivation of low-temperature expansions for Ising model. IX. High-field polynomials for the honeycomb-triangular system , 1975 .

[14]  J. Hammersley,et al.  Percolation Processes and Related Topics , 1963 .

[15]  D. Gaunt,et al.  Derivation of low‐temperature expansions for Ising model. IV. Two‐dimensional lattices‐temperature grouping , 1973 .

[16]  J. W. Essam,et al.  Derivation of Low‐Temperature Expansions for the Ising Model of a Ferromagnet and an Antiferromagnet , 1965 .

[17]  F. Harary,et al.  Chemical graphs—V : Enumeration and proposed nomenclature of benzenoid cata-condensed polycyclic aromatic hydrocarbons , 1968 .

[18]  J. Essam,et al.  The scaling laws for percolation processes , 1971 .

[19]  J. Essam,et al.  Percolation Processes. I. Low‐Density Expansion for the Mean Number of Clusters in a Random Mixture , 1966 .

[20]  J. W. Essam,et al.  Derivation of low‐temperature expansions for Ising model. III. Two‐dimensional lattices‐field grouping , 1973 .

[21]  J. W. Essam,et al.  Derivation of low-temperature expansions for Ising model. VI. Three-dimensional lattices-temperature grouping , 1973 .

[22]  J. S. Rowlinson,et al.  Phase Transitions and Critical Phenomena , 1972 .