Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

Abstract We introduce a generalized version of the noisy q-voter model, one of the most popular opinion dynamics models, in which voters can be in one of $$s \ge 2$$ s ≥ 2 states. As in the original binary q-voter model, which corresponds to $$s=2$$ s = 2 , at each update randomly selected voter can...

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Autores principales:	Bartłomiej Nowak, Bartosz Stoń, Katarzyna Sznajd-Weron
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/c61e3d35333b4b3ab12fd1e61f2aa369
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spelling	oai:doaj.org-article:c61e3d35333b4b3ab12fd1e61f2aa3692021-12-02T17:05:00ZDiscontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder10.1038/s41598-021-85361-92045-2322https://doaj.org/article/c61e3d35333b4b3ab12fd1e61f2aa3692021-03-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-85361-9https://doaj.org/toc/2045-2322Abstract We introduce a generalized version of the noisy q-voter model, one of the most popular opinion dynamics models, in which voters can be in one of $$s \ge 2$$ s ≥ 2 states. As in the original binary q-voter model, which corresponds to $$s=2$$ s = 2 , at each update randomly selected voter can conform to its q randomly chosen neighbors only if they are all in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act independently with probability p and with complementary probability $$1-p$$ 1 - p conform to others, and (2) quenched, which means that there is a fraction p of all voters, which are permanently independent and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo simulations. We show that for the number of states $$s>2$$ s > 2 the model displays discontinuous phase transitions for any $$q>1$$ q > 1 , on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for $$q>5$$ q > 5 . Moreover, unlike the case of $$s=2$$ s = 2 , for $$s>2$$ s > 2 discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one.Bartłomiej NowakBartosz StońKatarzyna Sznajd-WeronNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-13 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Bartłomiej Nowak Bartosz Stoń Katarzyna Sznajd-Weron Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder
description	Abstract We introduce a generalized version of the noisy q-voter model, one of the most popular opinion dynamics models, in which voters can be in one of $$s \ge 2$$ s ≥ 2 states. As in the original binary q-voter model, which corresponds to $$s=2$$ s = 2 , at each update randomly selected voter can conform to its q randomly chosen neighbors only if they are all in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act independently with probability p and with complementary probability $$1-p$$ 1 - p conform to others, and (2) quenched, which means that there is a fraction p of all voters, which are permanently independent and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo simulations. We show that for the number of states $$s>2$$ s > 2 the model displays discontinuous phase transitions for any $$q>1$$ q > 1 , on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for $$q>5$$ q > 5 . Moreover, unlike the case of $$s=2$$ s = 2 , for $$s>2$$ s > 2 discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one.
format	article
author	Bartłomiej Nowak Bartosz Stoń Katarzyna Sznajd-Weron
author_facet	Bartłomiej Nowak Bartosz Stoń Katarzyna Sznajd-Weron
author_sort	Bartłomiej Nowak
title	Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder
title_short	Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder
title_full	Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder
title_fullStr	Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder
title_full_unstemmed	Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder
title_sort	discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/c61e3d35333b4b3ab12fd1e61f2aa369
work_keys_str_mv	AT bartłomiejnowak discontinuousphasetransitionsinthemultistatenoisyqvotermodelquenchedvsannealeddisorder AT bartoszston discontinuousphasetransitionsinthemultistatenoisyqvotermodelquenchedvsannealeddisorder AT katarzynasznajdweron discontinuousphasetransitionsinthemultistatenoisyqvotermodelquenchedvsannealeddisorder
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Discontinuous phase transitions in the multi-state noisy q-voter model: quenched vs. annealed disorder

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