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Nonlinear q-voter model
Castellano, C; Muñoz, M A; Pastor Satorras, Romualdo
Universitat Politècnica de Catalunya. Departament de Física i Enginyeria Nuclear; Universitat Politècnica de Catalunya. SIMCON - Grup de Recerca de Simulació per Ordinador en Matèria Condensada
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.
Àrees temàtiques de la UPC::Física
Statistical physics
Física estadística
Attribution-NonCommercial-NoDerivs 3.0 Spain

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