1111.5626 (Hang Gu et al.)

Crossing on hyperbolic lattices    [PDF]

Hang Gu, Robert M. Ziff

We divide the circular boundary of a hyperbolic lattice into four intervals
of equal length, and study the probability of a percolation crossing between an
opposite pair of the intervals, as a function of the bond occupation
probability p. We consider the {7,3} (heptagonal), enhanced or extended binary
tree (EBT), the EBT dual, and {5,5} (pentagonal) lattices. We find that the
crossing probability increases gradually from zero to one as p increases from
the lower p_l to the upper p_u critical values. We find bounds and estimates
for the values of p_ l and p_u for these lattices, and identify the
self-duality point p* corresponding to where the crossing probability equals
1/2.

View original: http://arxiv.org/abs/1111.5626