Abstract
Abstract
We present an algorithm to compute the exact critical probability h(n) for an
n
×
∞
helical square lattice with random and independent site occupancy. The algorithm has time complexity
O
(
n
2
c
n
)
and space complexity
O
(
c
n
)
with c = 2.7459... and allows us to compute h(n) up to n = 24. Since the extrapolation result of h(n) is inconsistent with the current best estimation of pc
, we also compute and extend the exact critical probability
p
c
(
n
)
for an
n
×
∞
cylindrical square lattice to n = 24. Our calculation shows that the current best result of
p
c
=
0.592
746
050
792
10
(
2
)
by Jacobsen (2015 J. Phys. A: Math. Theor.
48 454003) is incorrect and the corrected value should be
0.592
746
050
7896
(
1
)
.
Funder
China Anhui Province Scientific Research Compilation Plan Project