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 -