Winding clusters in percolation on the Torus and the Moebius strip
arXiv:cond-mat/0310361 · doi:10.1023/B:JOSS.0000022376.25660.7b
Abstract
Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Moebius strip for different aspect ratios. The asynchronous parallelization of the simulation makes very large system and sample sizes possible. Our high accuracy results are fully consistent with predictions from conformal field theory. The numerical results for the Moebius strip and the number distribution of winding clusters on the torus await theoretical explanation. To our knowledge, this study is the first of its kind.
arXiv comment20 pages, 9 figures, submitted to J. Stat. Phys
References in corpus (10)
- A fast Monte Carlo algorithm for site or bond percolation
- Efficient Monte Carlo algorithm and high-precision results for percolation
- Critical Percolation in Finite Geometries
- On the Number of Incipient Spanning Clusters
- The Number of Incipient Spanning Clusters in Two-Dimensional Percolation
- Ising model on nonorientable surfaces: Exact solution for the Moebius strip and the Klein bottle
- Shape-dependent universality in percolation
- Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle
- Numerical results for crossing, spanning and wrapping in two-dimensional percolation
- Asynchronously parallelised percolation on distributed machines
Cited by in corpus (8)
- Freezing into Stripe States in Two-Dimensional Ferromagnets and Crossing Probabilities in Critical Percolation
- Fate of 2D Kinetic Ising Ferromagnets and Critical Percolation Crossing Probabilities
- Critical percolation in the dynamics of the 2d ferromagnetic Ising model
- Coarsening and percolation in the kinetic Ising model with spin exchange updates and the voter model
- Freezing in stripe states for kinetic Ising models: a comparative study of three dynamics
- Fate of Ising ferromagnets and antiferromagnets by zero-temperature Glauber dynamics on the two-dimensional Archimedean and 2-uniform lattices
- Anomalous Ising freezing times
- Continuum Percolation on Disoriented Surfaces: the Problem of Permeable Disks on a Klein Bottle