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), Barab\'asi-Albert (B-A), and Erdos-R\'enyi (E-R) networks, as well as their combinations. 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.