Percolation theory

Percolation and Conduction

1973 • 4,960 citations

The renormalization group and the ε expansion

1974 • 4,825 citations

An introduction to percolation theory

1971 • 2,532 citations

Scaling theory of percolation clusters

1979 • 2,306 citations

Some generalized order-disorder transformations

1952 • 2,022 citations

Percolation processes

1957 • 1,900 citations

Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm

1976 • 1,821 citations

Critical Exponents in 3.99 Dimensions

1972 • 1,547 citations

Critical Exponents for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-Vector Model in Three Dimensions from Field Theory

1977 • 1,177 citations

Correlation inequalities on some partially ordered sets

1971 • 1,147 citations

Exponents for the excluded volume problem as derived by the Wilson method

1972 • 1,003 citations

Solutions of Flexible Polymers. Neutron Experiments and Interpretation

1975 • 890 citations

A lower bound for the critical probability in a certain percolation process

1960 • 616 citations

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

1964 • 590 citations

Bootstrap percolation on a Bethe lattice

1979 • 560 citations

Some Cluster Size and Percolation Problems

1961 • 528 citations

Cluster shapes at the percolation threshold: and effective cluster dimensionality and its connection with critical-point exponents

1977 • 419 citations

Cluster size and boundary distribution near percolation threshold

1976 • 391 citations

Critical Percolation Probabilities by Series Methods

1964 • 314 citations

Application of the Padé Approximant Method to the Investigation of Some Magnetic Properties of the Ising Model

1961 • 308 citations

Ising-Model Critical Indices in Three Dimensions from the Callan-Symanzik Equation

1976 • 305 citations

Wilson theory for 2-dimensional Ising spin systems

1974 • 296 citations

A note on percolation

1978 • 274 citations

On the susceptibility of a ferromagnetic above the Curie point

1957 • 271 citations

Gelation in concentrated critically branched polymer solutions. Percolation scaling theory of intramolecular bond cycles

1976 • 270 citations

A real-space renormalization group for site and bond percolation

1977 • 264 citations

Percolation Processes and Related Topics

1963 • 262 citations

Excluded-Volume Problem and the Ising Model of Ferromagnetism

1959 • 258 citations

Percolation Probabilities on the Square Lattice

1978 • 255 citations

Renormalization-Group Approach to Percolation Problems

1975 • 249 citations

Critical properties of two tensor models with application to the percolation problem

1976 • 218 citations

Correlations in Ising Ferromagnets. II. External Magnetic Fields

1967 • 211 citations

Polymers and scaling

1976 • 204 citations

Numerical evaluations of the critical properties of the two-dimensional Ising model

1975 • 202 citations

Percolation Phenomena in Higher Dimensions: Approach to the Mean-Field Limit

1976 • 202 citations

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

1976 • 194 citations

Cell Growth Problems

1967 • 191 citations

Use of Series Expansions for the Ising Model Susceptibility and Excluded Volume Problem

1961 • 189 citations

Critical behaviour of the continuous n-component Potts model

1975 • 185 citations

New Type of Phase Transition

1974 • 175 citations

Percolation by position-space renormalisation group with large cells

1978 • 168 citations

Low-frequency response functions of random magnetic systems

1977 • 163 citations

Percolation points and critical point in the Ising model

1977 • 161 citations

Critical behavior of random resistor networks near the percolation threshold

1978 • 160 citations

Renormalization of the Potts model

1976 • 155 citations

Radius, perimeter, and density profile for percolation clusters and lattice animals

1979 • 151 citations

Weak Interactions and Eötvös Experiments

1976 • 148 citations

Cluster expansion for a polymer chain

1972 • 139 citations

Critical Probabilities for Cluster Size and Percolation Problems

1961 • 134 citations

Equivalence of the Critical Concentrations in the Ising and Heisenberg Models of Ferromagnetism

1960 • 130 citations

Percolation processes in three dimensions

1976 • 129 citations

Percolation processes in two dimensions. II. Critical concentrations and the mean size index

1976 • 125 citations

Percolation processes in d-dimensions

1976 • 124 citations

A renormalization group theory for percolation problems

1975 • 123 citations

Thermally driven phase transitions near the percolation threshold in two dimensions

1976 • 117 citations

Series expansion study of the pair connectedness in bond percolation models

1975 • 116 citations

Perspectives from the theory of phase transitions

1974 • 112 citations

Percolation in a lattice system with particle interaction

1974 • 112 citations

Essential singularity in percolation problems and asymptotic behavior of cluster size distribution

1978 • 110 citations

Bond percolation processes in d dimensions

1978 • 110 citations

The nature of percolation ‘channels’

1973 • 109 citations

Percolation and cluster distribution. II. layers, variable-range interactions, and exciton cluster model

1978 • 109 citations

Monte Carlo studies of percolation phenomena for a simple cubic lattice

1976 • 103 citations

Percolation and phase transitions in the Ising model

1976 • 99 citations

Spin Correlations near the Percolation Concentration in Two Dimensions

1976 • 99 citations

Amas accidentels dans les solutions solides désordonnées

1959 • 98 citations

Monte Carlo Study of Density Profile, Radius, and Perimeter for Percolation Clusters and Lattice Animals

1978 • 92 citations

Series expansions for the directed-bond percolation problem

1977 • 87 citations

Violation of Dynamical Scaling for Randomly Dilute Ising Ferromagnets near Percolation Threshold

1975 • 82 citations

Cluster Shape and Critical Exponents near Percolation Threshold

1976 • 81 citations

Random resistor tree in an applied field

1977 • 81 citations

Scaling theory of phase transitions in diluted systems near the percolation threshold

1977 • 80 citations

Renormalization-Group Approach to the Percolation Properties of the Triangular Ising Model

1978 • 77 citations

Strained mixed-cluster model for glass structure

1975 • 75 citations

A note on the mean size of clusters in the Ising model

1976 • 73 citations

Scaling form for percolation cluster sizes and perimeters

1978 • 72 citations

Ghost fields, pair connectedness, and scaling: exact results in one-dimensional percolation

1977 • 72 citations

Evidence for Fisher's Droplet Model in Simulated Two-Dimensional Cluster Distributions

1972 • 72 citations

The scaling laws for percolation processes

1971 • 67 citations

Lattice-lattice scaling and the generalized law of corresponding states

1971 • 67 citations

Linear and nonlinear relaxation and cluster dynamics near critical points

1976 • 66 citations

Lattice animals and percolation

1976 • 60 citations

Concept of the Long-Range Order in Percolation Problems

1970 • 60 citations

Site-cluster distributions and equation of state for the bond percolation model

1977 • 60 citations

Some cluster-size and percolation problems for interacting spins

1976 • 58 citations

Percolation processes in two dimensions IV. Percolation probability

1976 • 56 citations

Fluctuation Phenomena and Stochastic Processes

1959 • 54 citations

High-order behavior in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>field theories and the percolation problem

1978 • 53 citations

Spin models and cluster distributions for bond and site percolation models

1977 • 51 citations

Cluster shapes in lattice gases and percolation

1975 • 49 citations

Scaling theory for the pair-connectedness in percolation models

1975 • 48 citations

Shape and size of clusters in the Ising model

1977 • 46 citations

Percolation problems and phase transitions

1975 • 46 citations

Graph theory and statistical physics

1971 • 46 citations

Percolation processes in two dimensions. V. The exponent δ_pand scaling theory

1976 • 45 citations

Exact distribution of cluster size and perimeter for two-dimensional percolation

1976 • 42 citations

Mean number of clusters for percolation processes in two dimensions

1976 • 41 citations

Cluster statistics of the lattice gas model in three and two dimensions

1976 • 41 citations

Universality in the percolation problem—Anomalous dimensions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>operators

1977 • 40 citations

Some aspects of wetting/dewetting of a porous medium

1977 • 40 citations

Renormalization-group calculation of the critical exponents for percolation

1976 • 39 citations

Monte Carlo studies of two-dimensional percolation

1978 • 35 citations

Singularities of the dilute Ising ferromagnet

1974 • 35 citations

Cluster structure for dilute ferromagnets and percolation

1975 • 34 citations

Thermodynamic scaling laws for a dilute ferromagnet in the percolation limit by series methods

1976 • 33 citations

Site percolation as a Potts model

1977 • 31 citations

Spanning lengths of percolation clusters

1978 • 31 citations

Directed-bond percolation on hypercubic lattices

1977 • 31 citations

The percolation probability for the site problem on the face-centred cubic lattice

1976 • 30 citations

A test of scaling near the bond percolation threshold

1978 • 29 citations

Cluster and percolation inequalities for lattice systems with interactions

1977 • 29 citations

Series expansion study of the pair connectedness in site percolation models

1976 • 26 citations

Potts models, percolation, and duality

1979 • 25 citations

The percolation probability for the site problem on the triangular lattice

1974 • 24 citations

Series expansion study of the percolation probability for the triangular lattice bond problem

1978 • 23 citations

Scaling assumption for lattice animals in percolation theory

1978 • 23 citations

Confluent singularities and hyperscaling in the spin-¹/₂Ising model

1979 • 23 citations

The ramification of large clusters near percolation threshold

1978 • 22 citations

Upper bounds on cluster distribution functions and the nature of the Griffiths singularity

1978 • 22 citations

Renormalisation group approach for percolation-magnetic indices

1977 • 22 citations

A note on the convergence of the series expansion for the mean cluster size in random mixtures

1973 • 21 citations

Percolation theory in a gas

1977 • 19 citations

Temperature-Dependent Percolation Problem in the Bethe Lattice

1975 • 18 citations

Three properties of the infinite cluster in percolation theory

1978 • 16 citations

Percolation exponent δ_pfor lattice dimensionality d⩾3

1977 • 15 citations

Scaling function for cluster size distribution in two-dimensional site percolation

1978 • 15 citations

Speculations on the cluster radius below the percolation threshold

1978 • 14 citations

Critical behaviour of the percolation probability for the bond problem on a three dimensional lattice

1976 • 13 citations

Universality test for critical amplitudes in two dimensional percolation

1976 • 12 citations