Convergence of threshold estimates for two-dimensional percolation

Abstract

Using a recently introduced algorithm for simulating percolation in microcanonical (fixed-occupancy) samples, we study the convergence with increasing system size of a number of estimates for the percolation threshold for an open system with a square boundary, specifically for site percolation on a square lattice. We show that the convergence of the so-called "average-probability" estimate is described by a non-trivial correction-to-scaling exponent as predicted previously, and measure the value of this exponent to be 0.90(2). For the "median" and "cell-to-cell" estimates of the percolation threshold we verify that convergence does not depend on this exponent, having instead a slightly faster convergence with a trivial analytic leading exponent.

11 pages, 4 figures

References in corpus (1)

• A fast Monte Carlo algorithm for site or bond percolation

Cited by in corpus (30)

• Recent advances in percolation theory and its applications
• Scaling behavior of explosive percolation on the square lattice
• Tricritical point in explosive percolation
• Percolation on two- and three-dimensional lattices
• Pseudorandom Number Generators and the Square Site Percolation Threshold
• Gaussian model of explosive percolation in three and higher dimensions
• Percolation of the aligned dimers on a square lattice
• Complementary algorithms for graphs and percolation
• Rigorous confidence intervals for critical probabilities
• Finite-size scaling in asymmetric systems of percolating sticks
• About the fastest growth of Order Parameter in Models of Percolation
• Crossing on hyperbolic lattices
• Percolation thresholds on 3-dimensional lattices with 3 nearest neighbors
• Universality class of site and bond percolation on multi-multifractal scale-free planar stochastic lattice
• Newman-Ziff algorithm for the bootstrap percolation: application to the Archimedean lattices
• Site-Percolation Threshold of Carbon Nanotube Fibers: Fast Inspection of Percolation with Markov Stochastic Theory
• Dimer Covering and Percolation Frustration
• Bond percolation between $k$ separated points on a square lattice
• Comment on "Dynamic Opinion Model and Invasion Percolation"
• Universality class of the percolation in two-dimensional lattices with distortion
• Exact Percolation Probability on the Square Lattice
• Effect of chemical short-range order and percolation on passivation in binary alloys
• Exact percolation probabilities for a square lattice: Site percolation on a plane, cylinder, and torus
• Explosive percolation on scale-free multifractal weighted planar stochastic lattice
• Rigorous Confidence Intervals on Critical Thresholds in 3 Dimensions
• History-dependent percolation in two dimensions
• Geometric clusters in the overlap of the Ising model
• Characterizing spatial point processes by percolation transitions
• Universality of the Crossing Probability for the Potts Model for q=1,2,3,4
• The Tails of the Crossing Probability