Abstract
The scaling behavior for a binary fragmention of percolation clusters near a percolation threshold is investigated by a large cell Monte Carlo real space renormalization group method on two and three dimensions. We obtain the accurate values of critical exponents λ and ø describing the scaling of fragmentaion rate and the distribution of cluster masses produced by a binary fragmentation. Our results for λ and ø in two dimensions agree with the previous works, and we show in three dimensions that the fragmentation rate is also proportional to the cluster size. We provide the numerical evidence that the conjectured scaling relation σ = 1 + λ - ø is satisfied both in two and three dimensions where σ is the crossover exponent of the average cluster number in percolation theory.
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© 1998 Springer-Verlag Berlin Heidelberg
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Cheon, M., Chang, I. (1998). Fragmentation Scaling of the Percolation Cluster. In: Landau, D.P., Mon, K.K., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics X. Springer Proceedings in Physics, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46851-3_12
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DOI: https://doi.org/10.1007/978-3-642-46851-3_12
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