Percolation Thresholds and Fisher Exponents in Hypercubic Lattices

Abstract

We use invasion percolation to compute highly-accurate numerical values for bond and site percolation thresholds p_c on the hypercubic lattice Z^d for d = 4,,,,,13. We also compute the Fisher exponent tau governing the cluster size distribution at criticality. Our results support the claim that the mean-field value tau = 5/2 holds for d >= 6, with logarithmic corrections to power-law scaling at d=6.

References in corpus (9)

• Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices
• Simultaneous analysis of three-dimensional percolation models
• Critical Percolation in High Dimensions
• Percolation Threshold, Fisher Exponent, and Shortest Path Exponent for 4 and 5 Dimensions
• Correction-to-scaling exponent for two-dimensional percolation
• Simulation of percolation on massively-parallel computers
• Spreading with immunization in high dimensions
• Critical percolation clusters in seven dimensions and on a complete graph
• Percolation Thresholds in Hyperbolic Lattices

Cited by in corpus (27)

• Percolation on complex networks: Theory and application
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Percolation and the pandemic
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Bond percolation on simple cubic lattices with extended neighborhoods
• Efficient space virtualisation for Hoshen--Kopelman algorithm
• Precise bond percolation thresholds on several four-dimensional lattices
• Series Expansion of the Percolation Threshold on Hypercubic Lattices
• Geometric Upper Critical Dimensions of the Ising Model
• Critical exponents and universal excess cluster number of percolation in four and five dimensions
• Loss-tolerant architecture for quantum computing with quantum emitters
• $N$-cluster correlations in four- and five-dimensional percolation
• Jamming and percolation of dimers in restricted-valence random sequential adsorption
• Bond percolation between $k$ separated points on a square lattice
• Explosive percolation in finite dimensions
• High-dimensional percolation criticality and hints of mean-field-like caging of the random Lorentz gas
• Exact Percolation Probability on the Square Lattice
• Random site percolation thresholds on square lattice for complex neighborhoods containing sites up to the sixth coordination zone
• What are the limits of universality?
• Percolation thresholds on high dimensional $D_n$ and dense packing lattices
• Dynamics around the Site Percolation Threshold on High-Dimensional Hypercubic Lattices
• Percolation of sites not removed by a random walker in $d$ dimensions
• The fifty-year quest for universality in percolation theory in high dimensions
• On the monotonicity of the critical time in the Constrained-degree percolation model
• Fractal depth-first search paths in statistical physics models
• Multirange Ising model on the square lattice
• Extended-range percolation in five dimensions