Is Independence Necessary for a Discontinuous Phase Transition Within the -Voter Model?

Overview

Journal Entropy (Basel)

Publisher MDPI

Date 2020 Dec 3

PMID 33267234

Citations 5

Authors

Angelika Abramiuk

Jakub Pawlowski

Katarzyna Sznajd-Weron

Affiliations

Soon will be listed here.

Abstract

We ask a question about the possibility of a discontinuous phase transition and the related social hysteresis within the -voter model with anticonformity. Previously, it was claimed that within the -voter model the social hysteresis can emerge only because of an independent behavior, and for the model with anticonformity only continuous phase transitions are possible. However, this claim was derived from the model, in which the size of the influence group needed for the conformity was the same as the size of the group needed for the anticonformity. Here, we abandon this assumption on the equality of two types of social response and introduce the generalized model, in which the size of the influence group needed for the conformity q c and the size of the influence group needed for the anticonformity q a are independent variables and in general q c ≠ q a . We investigate the model on the complete graph, similarly as it was done for the original -voter model with anticonformity, and we show that such a generalized model displays both types of phase transitions depending on parameters q c and q a .

Citing Articles

Role of Time Scales in the Coupled Epidemic-Opinion Dynamics on Multiplex Networks.

Jankowski R, Chmiel A Entropy (Basel). 2022; 24(1).

PMID: 35052131 PMC: 8774805. DOI: 10.3390/e24010105.

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs.

Abramiuk-Szurlej A, Lipiecki A, Pawlowski J, Sznajd-Weron K Sci Rep. 2021; 11(1):17719.

PMID: 34489517 PMC: 8421341. DOI: 10.1038/s41598-021-97155-0.

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

Nowak B, Ston B, Sznajd-Weron K Sci Rep. 2021; 11(1):6098.

PMID: 33731793 PMC: 7971088. DOI: 10.1038/s41598-021-85361-9.

A Veritable Zoology of Successive Phase Transitions in the Asymmetric -Voter Model on Multiplex Networks.

Chmiel A, Sienkiewicz J, Fronczak A, Fronczak P Entropy (Basel). 2020; 22(9).

PMID: 33286787 PMC: 7597111. DOI: 10.3390/e22091018.

Cultural evolution of conformity and anticonformity.

Denton K, Ram Y, Liberman U, Feldman M Proc Natl Acad Sci U S A. 2020; 117(24):13603-13614.

PMID: 32461360 PMC: 7306811. DOI: 10.1073/pnas.2004102117.

References

Beekman M, Sumpter D, Ratnieks F . Phase transition between disordered and ordered foraging in Pharaoh's ants. Proc Natl Acad Sci U S A. 2001; 98(17):9703-6. PMC: 55516. DOI: 10.1073/pnas.161285298. View

Grinstein , Jayaprakash , He . Statistical mechanics of probabilistic cellular automata. Phys Rev Lett. 1985; 55(23):2527-2530. DOI: 10.1103/PhysRevLett.55.2527. View

Chen H, Shen C, Zhang H, Li G, Hou Z, Kurths J . First-order phase transition in a majority-vote model with inertia. Phys Rev E. 2017; 95(4-1):042304. DOI: 10.1103/PhysRevE.95.042304. View

Chmiel A, Sznajd-Weron K . Phase transitions in the q-voter model with noise on a duplex clique. Phys Rev E Stat Nonlin Soft Matter Phys. 2015; 92(5):052812. DOI: 10.1103/PhysRevE.92.052812. View

Nyczka P, Sznajd-Weron K, Cislo J . Phase transitions in the q-voter model with two types of stochastic driving. Phys Rev E Stat Nonlin Soft Matter Phys. 2012; 86(1 Pt 1):011105. DOI: 10.1103/PhysRevE.86.011105. View

Vieira A, Anteneodo C . Threshold q-voter model. Phys Rev E. 2018; 97(5-1):052106. DOI: 10.1103/PhysRevE.97.052106. View

Pruitt J, Berdahl A, Riehl C, Pinter-Wollman N, Moeller H, Pringle E . Social tipping points in animal societies. Proc Biol Sci. 2018; 285(1887). PMC: 6170811. DOI: 10.1098/rspb.2018.1282. View

Nyczka P, Byrka K, Nail P, Sznajd-Weron K . Conformity in numbers-Does criticality in social responses exist?. PLoS One. 2018; 13(12):e0209620. PMC: 6307709. DOI: 10.1371/journal.pone.0209620. View

Encinas J, Harunari P, de Oliveira M, Fiore C . Fundamental ingredients for discontinuous phase transitions in the inertial majority vote model. Sci Rep. 2018; 8(1):9338. PMC: 6008408. DOI: 10.1038/s41598-018-27240-4. View

10.

Doering G, Scharf I, Moeller H, Pruitt J . Social tipping points in animal societies in response to heat stress. Nat Ecol Evol. 2018; 2(8):1298-1305. DOI: 10.1038/s41559-018-0592-5. View

11.

Mobilia M . Nonlinear q-voter model with inflexible zealots. Phys Rev E Stat Nonlin Soft Matter Phys. 2015; 92(1):012803. DOI: 10.1103/PhysRevE.92.012803. View

12.

Mellor A, Mobilia M, Zia R . Heterogeneous out-of-equilibrium nonlinear q-voter model with zealotry. Phys Rev E. 2017; 95(1-1):012104. DOI: 10.1103/PhysRevE.95.012104. View

13.

Peralta A, Carro A, San Miguel M, Toral R . Analytical and numerical study of the non-linear noisy voter model on complex networks. Chaos. 2018; 28(7):075516. DOI: 10.1063/1.5030112. View

14.

Al Hammal O, Chate H, Dornic I, Munoz M . Langevin description of critical phenomena with two symmetric absorbing states. Phys Rev Lett. 2005; 94(23):230601. DOI: 10.1103/PhysRevLett.94.230601. View

15.

Watts D . A simple model of global cascades on random networks. Proc Natl Acad Sci U S A. 2006; 99(9):5766-71. PMC: 122850. DOI: 10.1073/pnas.082090499. View

16.

Castellano C, Munoz M, Pastor-Satorras R . Nonlinear q-voter model. Phys Rev E Stat Nonlin Soft Matter Phys. 2009; 80(4 Pt 1):041129. DOI: 10.1103/PhysRevE.80.041129. View

17.

Jedrzejewski A . Pair approximation for the q-voter model with independence on complex networks. Phys Rev E. 2017; 95(1-1):012307. DOI: 10.1103/PhysRevE.95.012307. View

18.

Argyle M . Social pressure in public and private situations. J Abnorm Psychol. 1957; 54(2):172-5. DOI: 10.1037/h0040490. View

19.

Vazquez F, Lopez C . Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior. Phys Rev E Stat Nonlin Soft Matter Phys. 2009; 78(6 Pt 1):061127. DOI: 10.1103/PhysRevE.78.061127. View