  We study the collective behavior of nonequilibrium systems subject to an
external field with a dynamics characterized by the existence of
non-interacting states. Aiming at exploring the generality of the results, we
consider two types of models according to the nature of their state variables:
(i) a vector model, where interactions are proportional to the overlap between
the states, and (ii) a scalar model, where interaction depends on the distance
between states. In both cases the system displays three phases: two ordered
phases, one parallel to the field, and another orthogonal to the field; and a
disordered phase. The phase space is numerically characterized for each model
in a fully connected network. By placing the particles on a small-world
network, we show that, while a regular lattice favors the alignment with the
field, the presence of long-range interactions promotes the formation of the
ordered phase orthogonal to the field.
