The impact of social noise on the majority rule model across various network topologies

We explore the impact of social noise, characterized by nonconformist behavior, on the phase transition within the framework of the majority rule model. The order–disorder transition can reflect the consensus-polarization state in a social context. This study covers various network topologies, including complete graphs, two-dimensional (2-D) square lattices, three-dimensional (3-D) square lattices, and heterogeneous or complex networks such as Watts–Strogatz (W–S), Barabási–Albert (B–A), and Erdős–Rényi (E–R) networks, as well as their combinations (multilayer network). Social behavior is represented by the parameter $p$, which indicates the probability of agents exhibiting nonconformist behavior. Our results show that the model exhibits a continuous phase transition across all networks. Through finite-size scaling analysis and evaluation of critical exponents, our results suggest that the model falls into the same universality class as the Ising model.