Shape-dependent universality in percolation

Abstract

The shape-dependent universality of the excess percolation cluster number and cross-configuration probability on a torus is discussed. Besides the aspect ratio of the torus, the universality class depends upon the twist in the periodic boundary conditions, which for example are generally introduced when triangular lattices are used in simulations.

11 pages, 3 figures, to be published in Physica A

References in corpus (3)

• Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices
• Universality of finite-size corrections to the number of critical percolation clusters
• Exact results at the 2-D percolation point

Cited by in corpus (35)

• A fast Monte Carlo algorithm for site or bond percolation
• Efficient Monte Carlo algorithm and high-precision results for percolation
• Recent advances and open challenges in percolation
• Scaling behavior of explosive percolation on the square lattice
• The Largest Cluster in Subcritical Percolation
• Percolation on two- and three-dimensional lattices
• High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class
• Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle
• Correction-to-scaling exponent for two-dimensional percolation
• Equivalent-neighbor percolation models in two dimensions: crossover between mean-field and short-range behavior
• Percolation in the canonical ensemble
• Winding clusters in percolation on the Torus and the Moebius strip
• Critical exponents for the homology of Fortuin-Kasteleyn clusters on a torus
• Stochastic Renormalization Group in Percolation: I. Fluctuations and Crossover
• Critical exponents and universal excess cluster number of percolation in four and five dimensions
• Universal features of cluster numbers in percolation
• Universal Critical Wrapping Probabilities in the Canonical Ensemble
• Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
• Percolation and critical O($n$) loop configurations
• Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems
• Percolation of the two-dimensional XY model in the flow representation
• Potts and percolation models on bowtie lattices
• Corrections to scaling for percolative conduction: anomalous behavior at small L
• Conducting-angle-based percolation in the XY model
• Percolation thresholds of randomly rotating patchy particles on Archimedean lattices
• Leaf-excluded percolation in two and three dimensions
• Excess number of percolation clusters on the surface of a sphere
• Universal crossing probability in anisotropic systems
• Enclosed area distribution in percolation
• Iterative Site Percolation on Triangular Lattice
• Universality of percolation at dynamic pseudocritical point
• Cluster Analysis of the Ising Model and Universal Finite-Size Scaling
• Inverse Cascade in Percolation Model: Hierarchical Description of Time-dependent Scaling
• Wrapping probabilities for Potts spin clusters on a torus
• Exact Results for Average Cluster Numbers in Bond Percolation on Infinite-Length Lattice Strips