  We study a contact process with creation at first- and second-neighbor sites
and inhibition at first neighbors, in the form of an annihilation rate that
increases with the number of occupied first neighbors. Mean-field theory
predicts three phases: inactive (absorbing), active symmetric, and active
asymmetric, the latter exhibiting distinct sublattice densities on a bipartite
lattice. These phases are separated by continuous transitions; the phase
diagram is reentrant. Monte Carlo simulations in two dimensions verify these
predictions qualitatively, except for a first-neighbor creation rate of zero.
(In the latter case one of the phase transitions is discontinuous.) Our
numerical results confirm that the symmetric-asymmetric transition belongs to
the Ising universality class, and that the active-absorbing transition belongs
to the directed percolation class, as expected from symmetry considerations.
