A reduction of the $\theta (p_c)=0$ problem to a conjectured inequality

Abstract

We conjecture a new correlation-like inequality for percolation probabilities and support our conjecture with numerical evidence and a few special cases which we prove. This inequality, if true, implies that there is no percolation at criticality on the Euclidean lattice, for any dimension bigger than one.

38 pages, 4 figures