Critical properties of random-site percolation in two and three dimensions: A Monte Carlo study

✍ Scribed by Martin Corsten; Naeem Jan; Robert Jerrard

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 645 KB
• Volume: 156
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(89)90020-4

✦ Synopsis

We measure the critical exponents of two-dimensional and three-dimensional random-site percolation and find excellent agreement with Nienhuis exact results (two-dimensions) and good agreement with other numerical work (three-dimensions).

We also measure the correlation length amplitude ratio and the mean-cluster size amplitude ratio in two-and threedimensions.

We report values of 4.0 5 0.5 (2d). 2.0 t-0.5 (3d) and 75 ( 14) (2d) and 8 ( ' 1) (3d) for the correlation length and the mean cluster size amplitude ratios respectively. A direct measurement is made of the fractal dimension, d,. At the critical point. p, (=O.SO) of the triangular lattice d, is 1.90 ? 0.01 while at p, = 0.3117 for the simple cubic lattice d, is 2.50 -t 0.02.