# Percolation and scaling on a quasilattice

@article{Lu1987PercolationAS, title={Percolation and scaling on a quasilattice}, author={Jian Ping Lu and Joseph L. Birman}, journal={Journal of Statistical Physics}, year={1987}, volume={46}, pages={1057-1066} }

We report results of a study of percolation on a two-dimensional Penrose quasilattice. After an extensive numerical analysis, we find that two-dimensional universality is obeyed. The scaling exponentsσ andτ have the values expected,τ=2.04 andσ=0.39, consistent with the universality class for percolation on a 2D periodic lattice. But the percolation thresholdpc=0.483, differs from other 2D lattices with the same average coordination number ¯z=4.

## 13 Citations

### Percolation in Penrose tiling and its dual: in Comparison with Analysis for Kagomé, Dice and Square lattices

- Materials Science
- 1988

### A proposal for the estimation of percolation thresholds in two-dimensional lattices

- Computer Science
- 1989

The authors propose a method to calculate percolation thresholds pc and their error bars Delta pc of two-dimensional (2D) lattices that enables them to estimate thresholds very accurately even when they use the MC data obtained from fairly small sizes.

### Real-space renormalization group approach to the Potts model on the two-dimensional Penrose tiling

- Physics
- 1999

### Aperiodic Ising Models

- Physics
- 1996

We consider several aspects of non-periodic Ising models in one and two dimensions. Here we are not interested in random systems, but rather in models with intrinsic long-range aperiodic order. The…

### Percolation on Penrose Tilings

- MathematicsCanadian Mathematical Bulletin
- 1998

Abstract In Bernoulli site percolation on Penrose tilings there are two natural definitions of the critical probability. This paper shows that they are equal on almost all Penrose tilings. It also…

### Percolation cluster statistics of Lennard-Jones fluids

- Physics
- 1989

The percolation and cluster characteristics of the 3D Lennard-Jones, LJ, fluid have been determined by molecular dynamics computer simulation. The continuous nature of the LJ potential has a…

### Supplementary material: Topological estimation of percolation thresholds

- Mathematics
- 2007

This is supplementary material for the article arxiv:0708.3250. We provide an alternative introduction of the mean Euler Characteristic, additional examples and the percolation thresholds for…

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