  We consider systems whose steady-states exhibit a nonequilibrium phase
transition from an active state to one -among an infinite number- absorbing
state, as some control parameter is varied across a threshold value. The pair
contact process, stochastic fixed-energy sandpiles, activated random walks and
many other cellular automata or reaction-diffusion processes are covered by our
analysis. We argue that the upper critical dimension below which anomalous
fluctuation driven scaling appears is d_c=6, in contrast to a widespread belief
(see Dickman cond-mat 0110043 for an overview). We provide the exponents
governing the critical behavior close to or at the transition point to first
order in a 6-d expansion.
