dc.contributor |
Universitat Politècnica de Catalunya. Departament de Física i Enginyeria Nuclear |
dc.contributor |
Universitat Politècnica de Catalunya. SIMCON - Grup de Recerca de Simulació per Ordinador en Matèria Condensada |
dc.contributor.author |
Castellano, C |
dc.contributor.author |
Muñoz, M A |
dc.contributor.author |
Pastor Satorras, Romualdo |
dc.date |
2009-10 |
dc.identifier.citation |
Castellano, C.; Muñoz, M.; Pastor, R. Nonlinear q-voter model. "Physical review E, statistical physics, plasmas, fluids, and related interdisciplinary topics", Octubre 2009, vol. 80, núm. 041129, p. 1-8. |
dc.identifier.citation |
1063-651X |
dc.identifier.uri |
http://hdl.handle.net/2117/7723 |
dc.language.iso |
eng |
dc.relation |
http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PLEEE8000080000004041129000001&idtype=cvips&prog=normal |
dc.rights |
Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.rights |
http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject |
Àrees temàtiques de la UPC::Física |
dc.subject |
Statistical physics |
dc.subject |
Física estadística |
dc.title |
Nonlinear q-voter model |
dc.type |
info:eu-repo/semantics/publishedVersion |
dc.type |
info:eu-repo/semantics/article |
dc.description.abstract |
We introduce a nonlinear variant of the voter model, the q-voter model, in which q neighbors (with possible repetition) are consulted for a voter to change opinion. If the q neighbors agree, the voter takes their opinion; if they do not have a unanimous opinion, still a voter can flip its state with probability ε. We solve the model
on a fully connected network (i.e., in mean field) and compute the exit probability as well as the average time to reach consensus by employing the backward Fokker-Planck formalism and scaling arguments. We analyze the results in the perspective of a recently proposed Langevin equation aimed at describing generic phase transitions in systems with two (Z2-symmetric) absorbing states. In particular, by deriving explicitly the coefficients of such a Langevin equation as a function of the microscopic flipping probabilities, we find that in mean field the q-voter model exhibits a disordered phase for high ε and an ordered one for low ε with three possible ways to go from one to the other: (i) a unique (generalized-voter-like) transition, (ii) a series of two consecutive transitions, one (Ising-like) in which the Z2 symmetry is broken and a separate one (in the directed-percolation class) in which the system falls into an absorbing state, and (iii) a series of two transitions, including an intermediate regime in which the final state depends on initial conditions. This third (so far unexplored) scenario, in which a type of ordering dynamics emerges, is rationalized and found to be specific of mean field, i.e., fluctuations are explicitly shown to wash it out in spatially extended systems. |