Critical Exponents of Master-Node Network Model

TL;DR

This paper investigates a social opinion dynamics model on a ring network with a master node, revealing a unique non-equilibrium phase transition and critical behavior that likely does not belong to existing universality classes.

Contribution

It introduces a novel master-node network model for opinion dynamics and analyzes its critical exponents, showing its distinct universality class.

Findings

Identified a continuous non-equilibrium phase transition to an absorbing state.

Determined static and dynamic critical exponents via finite size scaling.

Found the model's critical behavior likely does not match known universality classes.

Abstract

The dynamics of competing opinions in social network play an important role in society, with many applications in diverse social contexts as consensus, elections, morality and so on. Here we study a model of interacting agents connected in networks to analyze their decision stochastic process. We consider a first-neighbor interaction between agents in a one-dimensional network with a shape of ring topology. Moreover, some agents are also connected to a hub, or master node, that has preferential choice or bias. Such connections are quenched. As the main results, we observed a continuous non-equilibrium phase transition to an absorbing state as a function of control parameters. By using the finite size scaling method, we analyzed the static and dynamic critical exponents to show that this model probably cannot match any universality class already known.