TY - JOUR
T1 - Amplitude ratios and β estimates from general dimension percolation moments
AU - Adlert, Joan
AU - Aharony, Amnon
AU - Meir, Yigal
AU - Harrist, A. Brooks
PY - 1986/12/1
Y1 - 1986/12/1
N2 - Low concentration series are generated for moments of the percolation cluster size distribution, Tj=(sJ-') (s is the number of sites on a cluster) for j = 2,…, 8 and general dimensionality d. These diverge at pcas (FORMULA PRESENTED.), where (FORMULA PRESENTED.) is the gap exponent. The series yield new accurate values for Δand βΔ = 2.23 ± 0.05, 2.10 ± 0.04, 2.03 ± 0.05 and 946; = 0.44 ± 0.15, 0.66 ± 0.09, 0.83 ± 0.08 at d = 3, 4, 5. In addition, ratios of the form AjAk/AmAn„, with j+ k = m + n, are shown to be universal. New values for some of these ratios are evaluated from the series, from the e expansion (έ = 6 — d) and exactly (in d = 1 and on the Bethe lattice). The results are in excellent agreement with each other for all dimensions. Results for different lattices at d = 2, 3 agree very well. These amplitude ratios are much better behaved than other ratios considered in the past, and should thus be more useful in characterising percolating systems.
AB - Low concentration series are generated for moments of the percolation cluster size distribution, Tj=(sJ-') (s is the number of sites on a cluster) for j = 2,…, 8 and general dimensionality d. These diverge at pcas (FORMULA PRESENTED.), where (FORMULA PRESENTED.) is the gap exponent. The series yield new accurate values for Δand βΔ = 2.23 ± 0.05, 2.10 ± 0.04, 2.03 ± 0.05 and 946; = 0.44 ± 0.15, 0.66 ± 0.09, 0.83 ± 0.08 at d = 3, 4, 5. In addition, ratios of the form AjAk/AmAn„, with j+ k = m + n, are shown to be universal. New values for some of these ratios are evaluated from the series, from the e expansion (έ = 6 — d) and exactly (in d = 1 and on the Bethe lattice). The results are in excellent agreement with each other for all dimensions. Results for different lattices at d = 2, 3 agree very well. These amplitude ratios are much better behaved than other ratios considered in the past, and should thus be more useful in characterising percolating systems.
UR - http://www.scopus.com/inward/record.url?scp=2842594921&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/19/17/026
DO - 10.1088/0305-4470/19/17/026
M3 - מאמר
AN - SCOPUS:2842594921
VL - 19
SP - 3631
EP - 3643
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 17
ER -