Non-Equilibrium Phase Transitions Induced by Social Temperature in Kinetic Exchange Opinion Models on Regular Lattices

Abstract: In this work we study the critical behavior of a three-state opinion model in the presence of noise. This noise represents the independent behavior, that plays the role of social temperature. Each agent on a regular D-dimensional lattice has a probability $q$ to act as independent, i.e., he can choose his opinion independent of the opinions of his neighbors. Furthermore, with the complementary probability $1-q$ the agent interacts with a randomly chosen nearest neighbor through a kinetic exchange. Our numerical results suggest that the model undergoes nonequilibrium phase transitions at critical points $q_{c}$ that depend on the lattice dimension. These transitions are of order-disorder type, presenting the same critical exponents of the Ising model. The results also suggest that the upper critical dimension of the model is $D_{c}=4$, as for the Ising model. From the social point of view, with increasing number of social connections, it is easier to observe a majority opinion in the population.