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

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 Barabási--Albert, Erdős--Rényi, random regular, and Watts--Strogatz networks, the estimated critical exponents remain close to the mean-field values, suggesting mean-field-like universal behavior within the system sizes studied. The strongest shift of the critical point occurs for Watts--Strogatz networks, where clustering and local correlations make the ordered phase less stable. 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 primarily controls the location of the transition, while the collective-reversal mechanism largely preserves mean-field-like critical behavior.