Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

Abstract

We study the binary q-voter model with generalized anticonformity on random Erdős–Rényi graphs. In such a model, two types of social responses, conformity and anticonformity, occur with complementary probabilities and the size of the source of influence q_c in case of conformity is independent from the size of the source of influence q_a in case of anticonformity. For q_c=q_a=q the model reduces to the original q-voter model with anticonformity. Previously, such a generalized model was studied only on the complete graph, which corresponds to the mean-field approach. It was shown that it can display discontinuous phase transitions for q_c ge q_a + Delta q, where Delta q=4 for q_a le 3 and Delta q=3 for q_a>3. In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree langle krangle le 150 observed empirically in social networks. Using the pair approximation, as well as Monte Carlo simulations, we show that discontinuous phase transitions indeed can survive, even for relatively small values of langle krangle. Moreover, we show that for q_a < q_c - 1 pair approximation results overlap the Monte Carlo ones. On the other hand, for q_a ge q_c - 1 pair approximation gives qualitatively wrong results indicating discontinuous phase transitions neither observed in the simulations nor within the mean-field approach. Finally, we report an intriguing result showing that the difference between the spinodals obtained within the pair approximation and the mean-field approach follows a power law with respect to langle krangle, as long as the pair approximation indicates correctly the type of the phase transition.