Spontaneous ordering against an external field in nonequilibrium systems

TL;DR

This paper investigates how nonequilibrium systems with external fields can spontaneously form ordered states either aligned or orthogonal to the field, depending on the network topology and interaction type.

Contribution

It introduces two models with different state variables and demonstrates how network structure influences the emergence of orthogonal or aligned order.

Findings

Regular lattices favor alignment with the external field.

Long-range interactions promote orthogonal ordering.

Three distinct phases are identified in the models.

Abstract

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.