Uniform Boundedness of Critical Crossing Probabilities Implies Hyperscaling - Chayes, Jennifer; Borgs, Christian; Kesten, H.; Spencer, J. (1998)
We consider bond percolation on the d -dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent r 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.