Local versus global interactions in nonequilibrium transitions: A model of social dynamics

TL;DR

This paper investigates how local and global interactions, including external and autonomous fields, influence phase transitions in a nonequilibrium social dynamics model, revealing thresholds and effects of field uniformity on order-disorder behavior.

Contribution

It introduces a model analyzing the impact of various interacting fields on nonequilibrium phase transitions in social systems, highlighting differences between uniform and nonuniform fields.

Findings

Disorder increases with higher interaction probability with the field.

A threshold exists beyond which the system remains disordered.

Nonuniform fields expand the ordered regime compared to uniform fields.

Abstract

A nonequilibrium system of locally interacting elements in a lattice with an absorbing order-disorder phase transition is studied under the effect of additional interacting fields. These fields are shown to produce interesting effects in the collective behavior of this system. Both for autonomous and external fields, disorder grows in the system when the probability of the elements to interact with the field is increased. There exists a threshold value of this probability beyond which the system is always disordered. The domain of parameters of the ordered regime is larger for nonuniform local fields than for spatially uniform fields. However, the zero field limit is discontinous. In the limit of vanishingly small probability of interaction with the field, autonomous or external fields are able to order a system that would fall in a disordered phase under local interactions of the elements alone. We consider different types of fields which are interpreted as forms of mass media acting on a social system in the context of Axelrod's model for cultural dissemination.