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

Spontaneous ordering against an external field in nonequilibrium systems