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- W3181083867 abstract "We study the binary $q$-voter model with generalized anticonformity on random Erdős-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 $q_c ge q_a + Delta q$, 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 critical points 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." @default.
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- W3181083867 date "2021-07-07" @default.
- W3181083867 modified "2023-09-26" @default.
- W3181083867 title "Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs" @default.
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