Uniform Boundedness of Crossing Probabilities Implies Hyperscaling - Borgs, Christian; Chayes, Jennifer; Kesten, H.; Spencer, J. (Random Structures and Algorithms 15, 1998)
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.