Fragmentation scaling of percolation clusters in two and three dimensions: Large-cell Monte Carlo RG approach
Department of Physics,
Pusan National University - Pusan 609-735, Korea
Accepted: 22 January 1999
The scaling behavior for a binary fragmentation of critical percolation clusters is investigated by a large-cell Monte Carlo real-space renormalization group method in two and three dimensions. We obtain accurate values of critical exponents λ and ϕ describing the scaling of fragmentation rate and the distribution of fragments' masses produced by a binary fragmentation. Our results for λ and ϕ show that the fragmentation rate is proportional to the size of mother cluster, and the scaling relation conjectured by Edwards et al. to be valid for all dimensions is satisfied in two and three dimensions, where is the crossover exponent of the average cluster number in percolation theory, which excludes the other scaling relations.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions
© EDP Sciences, 1999