Influence of Cooperative Agents on the Dynamics and Social Entropy production of the Majority-vote Model

We investigate the cooperative behavior phenomena in social networks using anisotropic effects on the majority-vote model with noise. In our formulation, a given individual selects an opinion equal to the majority of its neighbors with probability 1 - μq and the opposite with probability μq. The parameter q is called the system noise and acts as a social temperature promoting the social disorder, whereas μ stands for the cooperative behavior intensity, stimulating collective agreement. In our numerical investigations, we set a fraction f of collaborative agents to have noise sensibility 0 < μ < 1, while the complementary fraction 1 - f follows the standard majority-vote dynamics, i. e., μ = 1. We perform Monte Carlo simulations and the mean-field analysis to estimate the critical noise parameter q_c(μ, f) on regular lattices and obtain the phase diagram of the model. We conclude that the critical social temperature is an increasing function of the anisotropic fraction f for different cooperative phenomena intensity μ. We also estimate the critical exponents β/ν, γ/ν, and 1/ν, and find that the presence of the cooperative agents does not affect the Ising universality class of the model.