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1.
David J. Bergman 《Journal of statistical physics》2003,111(1-2):171-199
Arguments are presented to demonstrate that exact equality relations exist between the critical exponents which characterize the macroscopic conductivity
e
and the macroscopic elastic stiffness moduli C
e
of percolating systems of any dimensionality. Using the notation
e
p
t
, C
e
p
T
for the critical behavior of a randomly diluted system slightly above the percolation threshold p
c
, (pp–p
c
>0) and
e
|p|–s
, C
e
|p|–S
for the critical behavior of a random mixture of normal and perfectly conducting or normal and perfectly rigid constituents slightly below that threshold, (pp–p
c
<0) we show that T=t+2 and S=s, where is the percolation correlation length critical exponent |p|–
(p0). 相似文献
2.
Charles M. Newman 《Journal of statistical physics》1987,47(5-6):695-699
The inequality in the title is derived for standard site percolation in any dimension, assuming only that the percolation density vanishes at the critical point. The proof, based on a lattice animal expansion, is fairly simple and is applicable to rather general (site or bond, short-or long-range) independent percolation models. 相似文献