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 $$q_c$$ q c in case of conformity is...

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Autores principales:	Angelika Abramiuk-Szurlej, Arkadiusz Lipiecki, Jakub Pawłowski, Katarzyna Sznajd-Weron
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/8e8a5a60939a463081442842ca63803a
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spelling	oai:doaj.org-article:8e8a5a60939a463081442842ca63803a2021-12-02T19:12:28ZDiscontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs10.1038/s41598-021-97155-02045-2322https://doaj.org/article/8e8a5a60939a463081442842ca63803a2021-09-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-97155-0https://doaj.org/toc/2045-2322Abstract 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 $$q_c$$ q c in case of conformity is independent from the size of the source of influence $$q_a$$ q a in case of anticonformity. For $$q_c=q_a=q$$ 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 $$q_c \ge q_a + \Delta q$$ q c ≥ q a + Δ q , where $$\Delta q=4$$ Δ q = 4 for $$q_a \le 3$$ q a ≤ 3 and $$\Delta q=3$$ Δ q = 3 for $$q_a>3$$ q a > 3 . In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree $$\langle k\rangle \le 150$$ ⟨ 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 $$\langle k\rangle$$ ⟨ k ⟩ . Moreover, we show that for $$q_a < q_c - 1$$ q a < q c - 1 pair approximation results overlap the Monte Carlo ones. On the other hand, for $$q_a \ge q_c - 1$$ 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 $$\langle k\rangle$$ ⟨ k ⟩ , as long as the pair approximation indicates correctly the type of the phase transition.Angelika Abramiuk-SzurlejArkadiusz LipieckiJakub PawłowskiKatarzyna Sznajd-WeronNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Angelika Abramiuk-Szurlej Arkadiusz Lipiecki Jakub Pawłowski Katarzyna Sznajd-Weron Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs
description	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 $$q_c$$ q c in case of conformity is independent from the size of the source of influence $$q_a$$ q a in case of anticonformity. For $$q_c=q_a=q$$ 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 $$q_c \ge q_a + \Delta q$$ q c ≥ q a + Δ q , where $$\Delta q=4$$ Δ q = 4 for $$q_a \le 3$$ q a ≤ 3 and $$\Delta q=3$$ Δ q = 3 for $$q_a>3$$ q a > 3 . In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree $$\langle k\rangle \le 150$$ ⟨ 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 $$\langle k\rangle$$ ⟨ k ⟩ . Moreover, we show that for $$q_a < q_c - 1$$ q a < q c - 1 pair approximation results overlap the Monte Carlo ones. On the other hand, for $$q_a \ge q_c - 1$$ 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 $$\langle k\rangle$$ ⟨ k ⟩ , as long as the pair approximation indicates correctly the type of the phase transition.
format	article
author	Angelika Abramiuk-Szurlej Arkadiusz Lipiecki Jakub Pawłowski Katarzyna Sznajd-Weron
author_facet	Angelika Abramiuk-Szurlej Arkadiusz Lipiecki Jakub Pawłowski Katarzyna Sznajd-Weron
author_sort	Angelika Abramiuk-Szurlej
title	Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs
title_short	Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs
title_full	Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs
title_fullStr	Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs
title_full_unstemmed	Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs
title_sort	discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/8e8a5a60939a463081442842ca63803a
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Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

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