Uniform boundedness of critical crossing probabilities implies hyperscaling

We consider bond percolation on the d-dimensional hypercubic lattice. Assum ing the existence of a single critical exponent, the exponent rho describin g the decay rate of point-to-plane crossings at the critical point, we prov e that hyperscaling holds whenever critical rectangle crossing probabilitie s are uniformly bounded away from 1. (C) 1999 John Wiley & Sons, Inc.