Topology-dependent criticality in triplet majority-rule dynamics with collective reversal

TL;DR

This paper investigates how different network topologies influence the critical behavior of a triplet majority-rule opinion dynamics model with collective reversal, revealing topology-dependent shifts in phase transition points and critical exponents.

Contribution

It demonstrates that quenched network topology significantly affects the critical point and effective critical behavior in opinion dynamics models with collective reversal.

Findings

Quenched topology shifts the order--disorder critical point from the well-mixed value.

Critical exponents remain close to mean-field values for Barabási–Albert, Erdős–Rényi, and random regular networks.

Watts–Strogatz networks show lower critical points and stronger deviations in critical exponents.

Abstract

We study a triplet majority-rule opinion-dynamics model with collective reversal on quenched networks. Interactions occur on local triplets composed of one agent and two of its neighbors, while collective reversal acts only on unanimous triplets. This rule separates local conformity from external perturbations that disrupt local agreement. We show that quenched network topology shifts the order--disorder critical point away from the well-mixed value. For Barab\'asi--Albert, Erd\H{o}s--R\'enyi, and random regular networks, the critical point is shifted while the critical exponents remain close to the mean-field values. By contrast, Watts--Strogatz networks exhibit a much lower critical point and stronger deviations in the effective critical exponents, highlighting the role of clustering and local correlations. A rewiring analysis of Watts--Strogatz networks further shows that the ordered phase becomes more stable as the network becomes more random. These results indicate that quenched topology not only sets the transition point, but also leads to topology-dependent effective critical behavior in networks with strong clustering and local correlations.