Hyperscaling Inequalities for the Contact Process and Oriented Percolation

The contact process and oriented percolation are expected to exhibit the same critical behavior in any dimension. Above their upper critical dimension d_c, they exhibit the same critical behavior as the branching process. Assuming existence of the critical exponents, we prove a pair of hyperscaling inequalities which, together with the results of refs. 16 and 18, implies d_c=4.