TY - JOUR
T1 - Density profile of the incipient infinite percolation cluster
AU - Stauffer, Dietrich
AU - Aharony, Amnon
PY - 1999/7
Y1 - 1999/7
N2 - Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance from the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact results in d = 2 and d = 6 - ∈ dimensions and with earlier simulations. We also present and explain results for bus-bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend on the aspect ratios of the samples.
AB - Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance from the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact results in d = 2 and d = 6 - ∈ dimensions and with earlier simulations. We also present and explain results for bus-bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend on the aspect ratios of the samples.
KW - Connectivity Function
KW - Critical Exponents
KW - Dimensionality Dependence
UR - http://www.scopus.com/inward/record.url?scp=0033476759&partnerID=8YFLogxK
U2 - 10.1142/S0129183199000735
DO - 10.1142/S0129183199000735
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AN - SCOPUS:0033476759
SN - 0129-1831
VL - 10
SP - 935
EP - 940
JO - International Journal of Modern Physics C
JF - International Journal of Modern Physics C
IS - 5
ER -