From discrete to continuous percolation in dimensions 3 to 7

Abstract

We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its continuous limit is controlled by a power-law dependency with a universal exponent $\theta =3/2$. This allows us to estimate the continuous percolation thresholds in a model of aligned hypercubes in dimensions $d=3,\dots ,7$ with accuracy far better than that attained using any other method before. We also report improved values of the correlation length critical exponent $\nu$ in dimensions $d=4,5$ and the values of several universal wrapping probabilities for $d=4,\dots ,7$.

References in corpus (6)

• Continuum Percolation Thresholds in Two Dimensions
• Simultaneous analysis of three-dimensional percolation models
• Effect of Dimensionality on the Continuum Percolation of Overlapping Hyperspheres and Hypercubes: II. Simulation Results and Analyses
• Simple cubic random-site percolation thresholds for neighborhoods containing fourth-nearest neighbors
• Percolation of overlapping squares or cubes on a lattice
• Dimensional study of the dynamical arrest in a random Lorentz gas

Cited by in corpus (30)

• Percolation on complex networks: Theory and application
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Measurement-induced criticality and entanglement clusters: a study of 1D and 2D Clifford circuits
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Percolation description of charge transport in amorphous oxide semiconductors
• Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit
• Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions
• Interplay between percolation and glassiness in the random Lorentz gas
• Bond percolation on simple cubic lattices with extended neighborhoods
• Jamming and percolation of $k^3$-mers on simple cubic lattices
• Jamming and percolation of $k^2$-mers on simple cubic lattices
• Critical exponents and universal excess cluster number of percolation in four and five dimensions
• $N$-cluster correlations in four- and five-dimensional percolation
• Site and bond percolation on four-dimensional simple hypercubic lattices with extended neighborhoods
• Random site percolation on honeycomb lattices with complex neighborhoods
• High-dimensional percolation criticality and hints of mean-field-like caging of the random Lorentz gas
• Critical p=1/2 in percolation on semi-infinite strips
• Random site percolation thresholds on square lattice for complex neighborhoods containing sites up to the sixth coordination zone
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; Resummation of perturbative renormalization functions from field theories
• Dynamics around the Site Percolation Threshold on High-Dimensional Hypercubic Lattices
• Critical properties of the Susceptible-Exposed-Infected model with correlated temporal disorder
• Time increasing rates of infiltration and reaction in porous media at the percolation thresholds
• Effect of shape anisotropy on percolation of aligned and overlapping objects on lattices
• Percolation of sites not removed by a random walker in $d$ dimensions
• Universality of random-site percolation thresholds for two-dimensional complex non-compact neighborhoods
• Universal correlations in percolation
• On the monotonicity of the critical time in the Constrained-degree percolation model
• Extended-range percolation in five dimensions
• Percolation in semicontinuum geometries