Effect of social behaviors in the opinion dynamics $q$-voter model

Abstract

Order-disorder phase transition is one of the interesting features in the opinion dynamics model of sociophysics. This phenomenon is caused by noise parameters, which can be treated as social responses such as anticonformity and independence in a social context. This paper explores the effect of anticonformity and independence in the occurrence of the order-disorder phase transition in the model. A probability $p$ represents anticonformity and independence, and the model is defined on the complete graph and two-dimensional (2D) square lattice. We also introduce a skepticism parameter represented by $s =\{0,1\}$, which describes a voter's propensity to behave independently and anticonformist. Our results analytically and numerically show that the model undergoes a continuous and discontinuous phase for all values of non-zero $s$ and at specific $q$-sized agent. No phase transition is observed in the model with independent voters on the 2D square lattice, and the model with anticonformist voters undergoes a continuous phase transition. We also analyze the effect of the probability $p$ and skepticism level $s$ on the outcome of the system's opinion.Comment: 15 pages and 16 figure