Nonequilibrium Opinion Spreading on 2D Small-World Networks

TL;DR

This paper investigates how opinions spread irreversibly on 2D small-world networks using a nonequilibrium kinetic model, revealing the effects of network shortcuts and temperature on opinion consensus and phase transitions.

Contribution

It introduces a nonequilibrium opinion spreading model on 2D small-world networks and analyzes the effects of network structure and temperature on opinion dynamics and phase transitions.

Findings

Shortcut fractions promote long-range order.

Temperature induces an order-disorder phase transition.

Critical exponents are determined via finite-size scaling.

Abstract

Irreversible opinion spreading phenomena are studied on small-world networks generated from 2D regular lattices by means of the magnetic Eden model, a nonequilibrium kinetic model for the growth of binary mixtures in contact with a thermal bath. In this model, the opinion or decision of an individual is affected by those of their acquaintances, but opinion changes (analogous to spin flips in an Ising-like model) are not allowed. Particularly, we focus on aspects inherent to the underlying 2D nature of the substrate, such as domain growth and cluster size distributions. Larger shortcut fractions are observed to favor long-range ordering connections between distant clusters across the network, while the temperature is shown to drive the system across an order-disorder transition, in agreement with previous investigations on related equilibrium spin systems. Furthermore, the extrapolated phase diagram, as well as the correlation length critical exponent, are determined by means of standard finite-size scaling procedures.