{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T15:13:46Z","timestamp":1785510826145,"version":"3.56.0"},"reference-count":52,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,19]],"date-time":"2020-01-19T00:00:00Z","timestamp":1579392000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["2016\/21\/B\/HS6\/01256"],"award-info":[{"award-number":["2016\/21\/B\/HS6\/01256"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We study the q-voter model with flexibility, which allows for describing a broad spectrum of independence from zealots, inflexibility, or stubbornness through noisy voters to self-anticonformity. Analyzing the model within the pair approximation allows us to derive the analytical formula for the critical point, below which an ordered (agreement) phase is stable. We determine the role of flexibility, which can be understood as an amount of variability associated with an independent behavior, as well as the role of the average network degree in shaping the character of the phase transition. We check the existence of the scaling relation, which previously was derived for the Sznajd model. We show that the scaling is universal, in a sense that it does not depend neither on the size of the group of influence nor on the average network degree. Analyzing the model in terms of the rescaled parameter, we determine the critical point, the jump of the order parameter, as well as the width of the hysteresis as a function of the average network degree     \u27e8 k \u27e9     and the size of the group of influence q.<\/jats:p>","DOI":"10.3390\/e22010120","type":"journal-article","created":{"date-parts":[[2020,1,20]],"date-time":"2020-01-20T04:27:09Z","timestamp":1579494429000},"page":"120","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Generalized Independence in the q-Voter Model: How Do Parameters Influence the Phase Transition?"],"prefix":"10.3390","volume":"22","author":[{"given":"Angelika","family":"Abramiuk","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1851-8508","authenticated-orcid":false,"given":"Katarzyna","family":"Sznajd-Weron","sequence":"additional","affiliation":[{"name":"Department of Theoretical Physics, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/0304-4149(94)00035-R","article-title":"The noisy voter model","volume":"55","author":"Granovsky","year":"1995","journal-title":"Stoch. 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