| Issue |
Europhys. Lett.
Volume 46, Number 1, April I 1999
|
|
|---|---|---|
| Page(s) | 6 - 12 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i1999-00554-7 | |
| Published online | 01 September 2002 | |
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
Received:
16
October
1998
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
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