We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.
|Original language||English (US)|
|Number of pages||46|
|Journal||Random Structures and Algorithms|
|State||Published - 1999|
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design
- Applied Mathematics