Nuclear Physics, Section B, ISSN 0550-3213, 1997, Volume 485, Issue 3, pp. 551 - 582

In critical percolation models, in a large cube there will typically be more than one cluster of comparable diameter. In 2D, the probability of k ⪢ 1 spanning...

Percolation | Incipient spanning clusters | Critical behavior | Incipient infinite cluster | Scaling limit | Hyperscaling | INFINITE CLUSTERS | INEQUALITIES | critical behavior | scaling limit | hyperscaling | UNIQUENESS | incipient spanning clusters | TRANSITION | PERCOLATION-THRESHOLD | PROBABILITY | CONTINUITY | percolation | MODELS | K UP PHYSICS, PARTICLES & FIELDS | incipient infinite cluster | CRITICAL-BEHAVIOR | 6 DIMENSIONS | PHYSICS, PARTICLES & FIELDS

Percolation | Incipient spanning clusters | Critical behavior | Incipient infinite cluster | Scaling limit | Hyperscaling | INFINITE CLUSTERS | INEQUALITIES | critical behavior | scaling limit | hyperscaling | UNIQUENESS | incipient spanning clusters | TRANSITION | PERCOLATION-THRESHOLD | PROBABILITY | CONTINUITY | percolation | MODELS | K UP PHYSICS, PARTICLES & FIELDS | incipient infinite cluster | CRITICAL-BEHAVIOR | 6 DIMENSIONS | PHYSICS, PARTICLES & FIELDS

Journal Article

PROBABILITY THEORY AND RELATED FIELDS, ISSN 0178-8051, 02/2020, Volume 176, Issue 1-2, pp. 533 - 597

We prove that the wired uniform spanning forest exhibits mean-field behaviour on a very large class of graphs, including every transitive graph of at least...

SCALING LIMITS | BEHAVIOR | Anomalous diffusion | ERASED RANDOM-WALK | PERCOLATION | VOLUME LIMIT | STATISTICS & PROBABILITY | INCIPIENT INFINITE CLUSTER | POLYNOMIAL-GROWTH | Random interlacements | INTERLACEMENTS | TREE | Uniform spanning tree | Mean-field | Critical exponents | Uniform spanning forest | Forests | Graph theory | Polynomials | Exponents | Avalanches

SCALING LIMITS | BEHAVIOR | Anomalous diffusion | ERASED RANDOM-WALK | PERCOLATION | VOLUME LIMIT | STATISTICS & PROBABILITY | INCIPIENT INFINITE CLUSTER | POLYNOMIAL-GROWTH | Random interlacements | INTERLACEMENTS | TREE | Uniform spanning tree | Mean-field | Critical exponents | Uniform spanning forest | Forests | Graph theory | Polynomials | Exponents | Avalanches

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 05/2017, Volume 50, Issue 23, p. 235001

We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based,...

universality | finite-size scaling | percolation | critical phenomena | hyperscaling | upper critical dimension | clusters | INFINITE CLUSTERS | NUMBER | LACE EXPANSION | PHYSICS, MULTIDISCIPLINARY | PHASE-TRANSITIONS | INCIPIENT SPANNING CLUSTERS | PHYSICS, MATHEMATICAL | CRITICAL RANDOM GRAPHS | UNIQUENESS | PROBABILITY | CRITICAL-BEHAVIOR | RANDOM SUBGRAPHS | Physics - Statistical Mechanics

universality | finite-size scaling | percolation | critical phenomena | hyperscaling | upper critical dimension | clusters | INFINITE CLUSTERS | NUMBER | LACE EXPANSION | PHYSICS, MULTIDISCIPLINARY | PHASE-TRANSITIONS | INCIPIENT SPANNING CLUSTERS | PHYSICS, MATHEMATICAL | CRITICAL RANDOM GRAPHS | UNIQUENESS | PROBABILITY | CRITICAL-BEHAVIOR | RANDOM SUBGRAPHS | Physics - Statistical Mechanics

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 7/2011, Volume 305, Issue 1, pp. 23 - 57

We study the simple random walk on the uniform spanning tree on $${\mathbb {Z}^2}$$ . We obtain estimates for the transition probabilities of the random walk,...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | FORESTS | ERASED RANDOM-WALK | GROWTH | EXPONENT | INCIPIENT INFINITE CLUSTER | PHYSICS, MATHEMATICAL | GRAPHS

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | FORESTS | ERASED RANDOM-WALK | GROWTH | EXPONENT | INCIPIENT INFINITE CLUSTER | PHYSICS, MATHEMATICAL | GRAPHS

Journal Article

Journal of the Physical Society of Japan, ISSN 0031-9015, 2007, Volume 76, Issue 3, pp. 034004 - 034004

We study statistical fluctuations of fractality of infinitely spanning clusters in bond percolation systems at the percolation threshold pc formed on...

critical phenomena | percolation transition | structural fluctuations | incipient clusters | fractal structures | Percolation transition | Incipient clusters | Fractal structures | Structural fluctuations | Critical phenomena | RENORMALIZATION-GROUP | NUMBER | LOCALIZED STATES | PHYSICS, MULTIDISCIPLINARY | STATISTICS | INCIPIENT SPANNING CLUSTERS | RARE EVENTS | MODELS | EXPONENT

critical phenomena | percolation transition | structural fluctuations | incipient clusters | fractal structures | Percolation transition | Incipient clusters | Fractal structures | Structural fluctuations | Critical phenomena | RENORMALIZATION-GROUP | NUMBER | LOCALIZED STATES | PHYSICS, MULTIDISCIPLINARY | STATISTICS | INCIPIENT SPANNING CLUSTERS | RARE EVENTS | MODELS | EXPONENT

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 01/2012, Volume 85, Issue 1, p. 011108

The percolation behavior of aligned rigid rods of length k (kmers) on two-dimensional square lattices has been studied by numerical simulations and finite-size...

SEQUENTIAL DEPOSITION | UNIVERSALITY | THRESHOLD | LONG RODS | PHYSICS, FLUIDS & PLASMAS | LINE SEGMENTS | INCIPIENT SPANNING CLUSTERS | NETWORKS | SITE-BOND PERCOLATION | ISING-MODELS | ADSORPTION | PHYSICS, MATHEMATICAL | Nanotubes - chemistry | Nanotubes - ultrastructure | Models, Chemical | Anisotropy | Computer Simulation | Models, Molecular | Crystallization - methods

SEQUENTIAL DEPOSITION | UNIVERSALITY | THRESHOLD | LONG RODS | PHYSICS, FLUIDS & PLASMAS | LINE SEGMENTS | INCIPIENT SPANNING CLUSTERS | NETWORKS | SITE-BOND PERCOLATION | ISING-MODELS | ADSORPTION | PHYSICS, MATHEMATICAL | Nanotubes - chemistry | Nanotubes - ultrastructure | Models, Chemical | Anisotropy | Computer Simulation | Models, Molecular | Crystallization - methods

Journal Article

The Annals of Probability, ISSN 0091-1798, 1/2003, Volume 31, Issue 1, pp. 444 - 485

We study several kinds of large critical percolation clusters in two dimensions. We show that from the microscopic (lattice scale) perspective these clusters...

Integers | Terminology | Gauge theory | Infinity | Rectangles | Mathematical lattices | Mathematics | Open star clusters | Vertices | Cylinders | Spanning cluster | Percolation | Critical phenomena | Incipient infinite cluster | percolation | HIGH-DIMENSIONAL PERCOLATION | critical phenomena | STATISTICS & PROBABILITY | incipient infinite cluster | SCALING LIMIT | spanning cluster | CRITICAL EXPONENTS | 82B43 | 60K35

Integers | Terminology | Gauge theory | Infinity | Rectangles | Mathematical lattices | Mathematics | Open star clusters | Vertices | Cylinders | Spanning cluster | Percolation | Critical phenomena | Incipient infinite cluster | percolation | HIGH-DIMENSIONAL PERCOLATION | critical phenomena | STATISTICS & PROBABILITY | incipient infinite cluster | SCALING LIMIT | spanning cluster | CRITICAL EXPONENTS | 82B43 | 60K35

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 05/2011, Volume 83, Issue 5, p. 051119

Random sequential adsorption of k-mers of different sizes and shapes deposited on two types of fractal surfaces (deterministic and statistical) is studied....

DIMENSIONS | PARTICLE DEPOSITION | MONOMERS | PHYSICS, FLUIDS & PLASMAS | BEHAVIOR | LINE SEGMENTS | PERCOLATION | PATTERNS | INCIPIENT SPANNING CLUSTERS | SELF-ORGANIZATION | PHYSICS, MATHEMATICAL | SURFACES

DIMENSIONS | PARTICLE DEPOSITION | MONOMERS | PHYSICS, FLUIDS & PLASMAS | BEHAVIOR | LINE SEGMENTS | PERCOLATION | PATTERNS | INCIPIENT SPANNING CLUSTERS | SELF-ORGANIZATION | PHYSICS, MATHEMATICAL | SURFACES

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 5/2004, Volume 115, Issue 3, pp. 839 - 853

Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Möbius strip for different aspect ratios. The...

torus | Physical Chemistry | Mathematical and Computational Physics | Monte-Carlo | conformal field theory | Quantum Physics | Möbius strip | 2D-percolation | Physics | Statistical Physics | Conformal field theory | Torus | 2-DIMENSIONAL PERCOLATION | UNIVERSALITY | PROBABILITY | NUMBERS | ALGORITHM | INCIPIENT SPANNING CLUSTERS | Mobius strip | PHYSICS, MATHEMATICAL

torus | Physical Chemistry | Mathematical and Computational Physics | Monte-Carlo | conformal field theory | Quantum Physics | Möbius strip | 2D-percolation | Physics | Statistical Physics | Conformal field theory | Torus | 2-DIMENSIONAL PERCOLATION | UNIVERSALITY | PROBABILITY | NUMBERS | ALGORITHM | INCIPIENT SPANNING CLUSTERS | Mobius strip | PHYSICS, MATHEMATICAL

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 01/2002, Volume 65, Issue 1, p. 016119/9

We investigate the final state of zero-temperature Ising ferromagnets that are endowed with single-spin-flip Glauber dynamics. Surprisingly, the ground state...

INTERACTING KINKS | DOMAIN GROWTH | PHYSICS, FLUIDS & PLASMAS | BOOTSTRAP PERCOLATION | STATISTICAL DYNAMICS | SYSTEMS | INCIPIENT SPANNING CLUSTERS | MODEL | PHASE-ORDERING KINETICS | PHYSICS, MATHEMATICAL | ZERO-TEMPERATURE DYNAMICS | 2 DIMENSIONS | Physics - Statistical Mechanics

INTERACTING KINKS | DOMAIN GROWTH | PHYSICS, FLUIDS & PLASMAS | BOOTSTRAP PERCOLATION | STATISTICAL DYNAMICS | SYSTEMS | INCIPIENT SPANNING CLUSTERS | MODEL | PHASE-ORDERING KINETICS | PHYSICS, MATHEMATICAL | ZERO-TEMPERATURE DYNAMICS | 2 DIMENSIONS | Physics - Statistical Mechanics

Journal Article

Physical Review Letters, ISSN 0031-9007, 03/2001, Volume 86, Issue 10, pp. 2134 - 2137

We study the finite-size scaling properties of the Ising model on the Mobius strip and the Klein bottle. The results are compared with those of the Ising model...

NUMBER | UNIVERSAL | PHYSICS, MULTIDISCIPLINARY | PERCOLATION | ANYONS | SYSTEMS | INCIPIENT SPANNING CLUSTERS | FREE-ENERGY | BRAID GROUP

NUMBER | UNIVERSAL | PHYSICS, MULTIDISCIPLINARY | PERCOLATION | ANYONS | SYSTEMS | INCIPIENT SPANNING CLUSTERS | FREE-ENERGY | BRAID GROUP

Journal Article

Electronic Journal of Probability, ISSN 1083-6489, 2013, Volume 18, pp. 1 - 20

Consider critical percolation in two dimensions. Under the condition that there are k disjoint alternating black and white arms crossing the annulus A (l, n),...

Arm events | Central limit theorem | Critical percolation | Incipient infinite cluster | Winding angle | Martingale | arm events | central limit theorem | CONFORMAL-INVARIANCE | ERASED RANDOM-WALKS | UNIFORM SPANNING-TREES | critical percolation | winding angle | martingale | STATISTICS & PROBABILITY | incipient infinite cluster | 2 DIMENSIONS

Arm events | Central limit theorem | Critical percolation | Incipient infinite cluster | Winding angle | Martingale | arm events | central limit theorem | CONFORMAL-INVARIANCE | ERASED RANDOM-WALKS | UNIFORM SPANNING-TREES | critical percolation | winding angle | martingale | STATISTICS & PROBABILITY | incipient infinite cluster | 2 DIMENSIONS

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 12/2013, Volume 392, Issue 24, pp. 6330 - 6340

A generalization of the pure site and pure bond percolation problems called site–bond percolation on a triangular lattice is studied. Motivated by...

Percolation | Phase transitions | Monte Carlo simulation | 2-DIMENSIONAL LATTICES | NUMBER | PHYSICS, MULTIDISCIPLINARY | INCIPIENT SPANNING CLUSTERS | MODEL | THRESHOLDS | Monte Carlo method | Analysis

Percolation | Phase transitions | Monte Carlo simulation | 2-DIMENSIONAL LATTICES | NUMBER | PHYSICS, MULTIDISCIPLINARY | INCIPIENT SPANNING CLUSTERS | MODEL | THRESHOLDS | Monte Carlo method | Analysis

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 2000, Volume 281, Issue 1, pp. 233 - 241

The recent progress in the study of finite-size scaling (FSS) properties of the Ising model is briefly reviewed. We calculate the universal FSS functions for...

Ising model | Percolation | Universality | Finite-size scaling | universality | 2-DIMENSIONAL PERCOLATION | SITE | finite-size scaling | NUMBER | percolation | PHYSICS, MULTIDISCIPLINARY | PLANAR LATTICES | SYSTEMS | INCIPIENT SPANNING CLUSTERS | Physics - Statistical Mechanics

Ising model | Percolation | Universality | Finite-size scaling | universality | 2-DIMENSIONAL PERCOLATION | SITE | finite-size scaling | NUMBER | percolation | PHYSICS, MULTIDISCIPLINARY | PLANAR LATTICES | SYSTEMS | INCIPIENT SPANNING CLUSTERS | Physics - Statistical Mechanics

Journal Article

PHYSICAL REVIEW E, ISSN 2470-0045, 11/2019, Volume 100, Issue 5

The percolation behavior of aligned rigid rods of length k (k-mers) on two-dimensional triangular lattices has been studied by numerical simulations and...

SQUARE | NUMBER | PROTEIN ADSORPTION | CONDUCTIVITY | PHYSICS, FLUIDS & PLASMAS | INCIPIENT SPANNING CLUSTERS | RANDOM SEQUENTIAL ADSORPTION | MODEL | PHYSICS, MATHEMATICAL | CARBON NANOTUBES

SQUARE | NUMBER | PROTEIN ADSORPTION | CONDUCTIVITY | PHYSICS, FLUIDS & PLASMAS | INCIPIENT SPANNING CLUSTERS | RANDOM SEQUENTIAL ADSORPTION | MODEL | PHYSICS, MATHEMATICAL | CARBON NANOTUBES

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 12/2013, Volume 392, Issue 23, pp. 5879 - 5887

In the present paper, patterns of diffusion-limited aggregation (DLA) grown on nonuniform substrates are investigated by means of Monte Carlo simulations. We...

DLA | Monte Carlo method | Fractals | Adsorption | Computer simulations | Carlo method | Monte | CONTROLLED CLUSTER FORMATION | 2-DIMENSIONAL PERCOLATION | DISPERSIONS | PHYSICS, MULTIDISCIPLINARY | SQUARE LATTICE | INCIPIENT SPANNING CLUSTERS | CONTROLLED DEPOSITION | SEDIMENT VOLUME | FLOC FORMATION | COMPUTER-SIMULATION | SURFACES

DLA | Monte Carlo method | Fractals | Adsorption | Computer simulations | Carlo method | Monte | CONTROLLED CLUSTER FORMATION | 2-DIMENSIONAL PERCOLATION | DISPERSIONS | PHYSICS, MULTIDISCIPLINARY | SQUARE LATTICE | INCIPIENT SPANNING CLUSTERS | CONTROLLED DEPOSITION | SEDIMENT VOLUME | FLOC FORMATION | COMPUTER-SIMULATION | SURFACES

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 01/2013, Volume 392, Issue 1, pp. 149 - 156

A theoretical approach, based on exact calculations of configurations on finite rectangular cells, is applied to study the percolation of homonuclear dimers on...

Percolation | Scaling phenomena | Multisite occupancy | Critical exponents | SEQUENTIAL DEPOSITION | RENORMALIZATION-GROUP | 2-DIMENSIONAL PERCOLATION | NUMBER | PARTICLES | PHYSICS, MULTIDISCIPLINARY | BOND PERCOLATION | INCIPIENT SPANNING CLUSTERS | ADSORPTION | MONTE-CARLO | ISING-MODEL | Analysis | Algorithms

Percolation | Scaling phenomena | Multisite occupancy | Critical exponents | SEQUENTIAL DEPOSITION | RENORMALIZATION-GROUP | 2-DIMENSIONAL PERCOLATION | NUMBER | PARTICLES | PHYSICS, MULTIDISCIPLINARY | BOND PERCOLATION | INCIPIENT SPANNING CLUSTERS | ADSORPTION | MONTE-CARLO | ISING-MODEL | Analysis | Algorithms

Journal Article

Journal of Experimental and Theoretical Physics Letters, ISSN 0021-3640, 10/2002, Volume 76, Issue 7, pp. 475 - 480

The probabilities of clusters spanning a hypercube of dimension two to seven along one axis of a percolation system under criticality were investigated...

Elementary Particles and Nuclei | Solid State Physics and Spectroscopy | Atoms, Molecules, Clusters and Plasmas | Physics | PROBABILITY | NUMBER | INCIPIENT SPANNING CLUSTERS | PHYSICS, MULTIDISCIPLINARY | ALGORITHM

Elementary Particles and Nuclei | Solid State Physics and Spectroscopy | Atoms, Molecules, Clusters and Plasmas | Physics | PROBABILITY | NUMBER | INCIPIENT SPANNING CLUSTERS | PHYSICS, MULTIDISCIPLINARY | ALGORITHM

Journal Article

Physics-Uspekhi, ISSN 1063-7869, 2012, Volume 55, Issue 7, pp. 733 - 738

Journal Article

PHYSICAL REVIEW E, ISSN 1539-3755, 09/1999, Volume 60, Issue 3, pp. 2716 - 2720

Based on the connection between the Ising model and a correlated percolation model, we calculate the distribution function for the fraction (c) of lattice...

DILUTE POTTS-MODEL | 2-DIMENSIONAL PERCOLATION | SITE | NUMBER | UNIVERSAL | PHYSICS, FLUIDS & PLASMAS | PLANAR LATTICES | INCIPIENT SPANNING CLUSTERS | PHYSICS, MATHEMATICAL

DILUTE POTTS-MODEL | 2-DIMENSIONAL PERCOLATION | SITE | NUMBER | UNIVERSAL | PHYSICS, FLUIDS & PLASMAS | PLANAR LATTICES | INCIPIENT SPANNING CLUSTERS | PHYSICS, MATHEMATICAL

Journal Article

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