https://doi.org/10.1007/PL00011059
Series expansion study of quantum percolation on the square lattice
1
School of Physics and Astronomy,
Raymond and Beverly Sackler Faculty of Exact Sciences,
Tel Aviv University,
69978 Tel Aviv, Israel
2
Department of Physics,
Pusan National University, Pusan 609-735, Korea
Received:
28
February
2000
Published online: 15 July 2000
We study the site and bond quantum percolation model on the
two-dimensional square lattice using series expansion in the low
concentration limit. We calculate series for the averages of
, where 
is the transmission
coefficient between sites i and j, for k=0, 1, 
,
5 and for several values of the energy E near the center of the band.
In the bond case the series are of order p14 in the concentration p
(some of those have been formerly available to order p10) and in
the site case of order p16. The analysis, using the Dlog-Padé approximation
and the techniques known as M1 and M2, shows clear evidence for a
delocalization transition (from exponentially localized to extended
or power-law-decaying states) at an energy-dependent threshold 
in
the range 
, confirming previous results
(e.g.
and 
for bond and site percolation) but in contrast with the Anderson
model. The divergence of the series for different k
is characterized by a constant gap exponent, which is identified as the
localization length exponent ν from a general scaling assumption.
We obtain estimates of 
. These values
violate the bound 
of Chayes et al.
PACS: 72.15.Rn – Localization effects (Anderson or weak localization) / 05.70.Jk – Critical point phenomena / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
