Critical behavior effects of Fractal Networks on the Majority-vote Model Dynamics

In this work, we investigate the impacts of Sierpinski fractal social networks with periodic boundary conditions in the dynamics and critical behavior of the two-state majority-vote model with noise. Here, each individual of a social community agrees with the majority of their neighbors with probability 1 – q and opposes them with the complementary chance q. The parameter q is the noise parameter and functions as a social temperature promoting the social disorder of the complex system. Similarly, the fractal dilution of the network of social interactions generates social-heat traps that favor nonconformist opinions against the majority of society. We perform Monte Carlo simulations to evaluate the order parameter or magnetization, the magnetic susceptibility, and the Binder fourth-order cumulant in three Sierpinski fractal networks with different sizes. We find that the model undergoes a second-order phase transition for a critical value of the noise parameter q_c, which depends on the fractal structure. We estimate the critical social temperature parameter q_c and the critical exponents β/ν, γ/ν and 1/ν of the majority-vote model on each fractal lattice.