Abstract
We study the collective behavior of non-equilibrium systems subjected 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 model 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 interactions depend on the distance between states. The phase space is numerically characterized for each model in a fully connected network and in random and scale-free networks. For both models, the system displays three phases: two ordered phases, one parallel to the field and another orthogonal to the field, and one disordered phase. By placing the particles on a small-world network, we show that an ordered phase in a state different from the one imposed by the field is possible because of the long-range interactions that exist in fully connected, random and scale-free networks. This phase does not exist in a regular lattice and emerges when long-range interactions are included in a small-world network.
Highlights
The collective behavior of the vector model on a fully connected network subject to an external field can be characterized by three phases on the space of parameters (q, B), as shown in figure 2: (I) an ordered phase induced by the field for q < q∗, for which σ = 0 and S = SM ∼ 1; (II) an ordered phase in a state orthogonal to the field (i. e. the overlap between the ordered state and the external field is zero) for q∗ < q < qc, for which σ increases and S > SM, with S ∼ 1; and (III) a disordered phase for q > qc, for which σ decreases and S → 0, SM → 0
We have addressed the question of the competition between collective selforganization and external forcing in non-equilibrium dynamics, as well as the role of network topology in this competition
We have considered two non-equilibrium models with a common feature: the existence of non-interacting states in their dynamics
Summary
The first system that we consider is based on the dynamics of cultural dissemination of the Axelrod model [23]. The collective behavior of the vector model on a fully connected network subject to an external field can be characterized by three phases on the space of parameters (q, B), as shown in figure 2: (I) an ordered phase induced by the field for q < q∗, for which σ = 0 and S = SM ∼ 1; (II) an ordered phase in a state orthogonal to the field For parameter values q < qc for which the system orders due to the interactions among the particles, a sufficiently weak external field is always able to impose its state to the entire system (phase I).
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