  The properties of the absorbing states of non-equilibrium models belonging to
the conserved directed percolation universality class are studied. We find that
at the critical point the absorbing states are hyperuniform, exhibiting
anomalously small density fluctuations. The exponent characterizing the
fluctuations is measured numerically, a scaling relation to other known
exponents is suggested, and a new correlation length relating to this ordering
is proposed. These results may have relevance to photonic band-gap materials.
