Uniform Boundedness of Critical Crossing Probabilities Implies Hyperscaling
- Jennifer Chayes ,
- Christian Borgs ,
- H. Kesten ,
- J. Spencer
MSR-TR-98-26 |
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.