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 Erdos-Renyi 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) >= q(a) + Delta q, where Delta q = 4 for q(a) <= 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 < k > <= 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 < k >. 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) >= 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 < k >, as long as the pair approximation indicates correctly the type of the phase transition.

Automated summary

A study was conducted on the binary q-voter model with generalized anticonformity on random Erdos-Renyi graphs, showing that discontinuous phase transitions can survive even for relatively small values of average node degree. The pair approximation results aligned with Monte Carlo simulations, but indicated qualitatively wrong results when q(a) >= q(c) - 1, suggesting that discontinuous phase transitions were not observed in simulations or in the mean-field approach. Additionally, a power law relationship was found between the spinodals obtained within the pair approximation and the mean-field approach, as long as the pair approximation correctly indicated the type of phase transition.