Phase transition in the majority rule model with the nonconformist agents

Independence and anticonformity are two types of social behaviors known in psychology literature the most studied parameters opinion dynamics model. These responsible for continuous (second-order) discontinuous (first-order) phase transition phenomena. Here, we investigate majority rule model which agents adopt independence behaviors. We define on several graphs: complete graph, two-dimensional (2D) square lattice, one-dimensional (1D) chain. By defining $p$ as a probability (or anticonformity), observe graph undergoes where critical points $p_c \approx 0.334$ ($p_c\approx 0.667$) with independent (anticonformist) agents. On 2D also at 0.0608$ ($p_c 0.4035$) 1D chain, there is no either or anticonformity. Furthermore, aid finite-size scaling analysis, obtain same sets exponents both models involving anticonformist graph. Therefore they identical to mean-field Ising However, case have different not Our work implies that existence behavior society makes it more challenging achieve consensus compared anticonformists.