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 [Formula: see text]-dimensional lattice has a probability [Formula: see text] to act as independent, i.e., he can choose his opinion independent of the opinions of his neighbors. Furthermore, with the complementary probability [Formula: see text], the agent interacts with a randomly chosen nearest neighbor through a kinetic exchange. Our numerical results suggest that the model undergoes non-equilibrium phase transitions at critical points [Formula: see text] 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 [Formula: see text], 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.
Highlights
In the last years, several models of opinion dynamics were studied in order to analyze social phenomena like polarization, extremism, conformity, and others.[1,2] social systems are interesting even from the theoretical point of view: they exhibit rich emergent phenomena, that results from the interaction of a large number of agents
Social systems are interesting even from the theoretical point of view: they exhibit rich emergent phenomena, that results from the interaction of a large number of agents. This interdisciplinary topic is usually treated by means of computer simulations of agent-based models, which allow us to understand the emergence of collective phenomena in those systems
This is an Open Access article published by World Scientic Publishing Company
Summary
Several models of opinion dynamics were studied in order to analyze social phenomena like polarization, extremism, conformity, and others.[1,2] social systems are interesting even from the theoretical point of view: they exhibit rich emergent phenomena, that results from the interaction of a large number of agents. We study the impact of independence on agents' behavior in a kinetic exchange opinion model (KEOM) dened on regular D-dimensional lattices. In the mean- ̄eld case, the model with competitive interactions[15] presents an order–disorder transition at pc 1⁄4 1=4, with the same exponents of the mean- ̄eld Ising model, namely 1⁄4 0:5, 1⁄4 1 and 1⁄4 2.a In the case of a square and cubic lattices, the KEOM with competitive interactions was studied recently: it undergoes a non-equilibrium phase transition at pc % 0:134 (for the two-dimensional square lattice) and pc % 0:199 (for the three-dimensional cubic lattice), and in the absence of negative interactions (p 1⁄4 0), the population reaches consensus states with all opinions þ1 or À1.16 For pc p 1:0, the society is in a paramagnetic disordered state, with an equal fraction of the two extreme opinions þ1 and À1 (on average). We will show that the independent behavior works as a noise that induces a phase transition in the KEOM with the absence of negative interactions
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