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

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 [Formula: see text] in case of conformity is independent from the size of the source of influence [Formula: see text] in case of anticonformity. For [Formula: see text] 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 [Formula: see text], where [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text]. In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree [Formula: see text] 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 [Formula: see text]. Moreover, we show that for [Formula: see text] pair approximation results overlap the Monte Carlo ones. On the other hand, for [Formula: see text] 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 [Formula: see text], as long as the pair approximation indicates correctly the type of the phase transition.