https://doi.org/10.1007/s100510050179
Topology invariance in percolation thresholds
Laboratoire des Milieux Désordonnés et
Hétérogènes (Laboratoire de l'Université
P. et M. Curie, Paris 6, associé au CNRS (URA n 800)) ,
Tour 13, Case 86, 4 place Jussieu, 75252 Paris Cedex 05, France
Corresponding author: a galam@ccr.jussieu.fr
Received:
7
July
1997
Accepted:
5
November
1997
Published online: 15 January 1998
An universal invariant for
site and bond percolation thresholds
(pcs and pcb respectively)
is proposed. The invariant writes
where 
and δ are positive constants,
and d the space dimension.
It is independent of the coordination number, thus exhibiting a topology
invariance at any d.
The formula is checked against
a large class of percolation problems, including
percolation
in non-Bravais lattices and in aperiodic lattices as well as rigid percolation.
The invariant is satisfied
within a relative error of 
for all the twenty lattices of our sample
at d=2, d=3, plus all hypercubes up to d=6.
PACS: 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems / 64.70.Pf – Glass transitions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998
