The European Physical Journal B

, Volume 71, Issue 4, pp 557–564 | Cite as

Consensus and ordering in language dynamics

  • X. CastellóEmail author
  • A. Baronchelli
  • V. Loreto
Topical issue on The Physics Approach to Risk: Agent-Based Models and Networks


We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB) state. Proposed in the context of language competition and emergence, the AB state was associated with bilingualism and synonymy respectively. We show that the two models are equivalent in the mean field approximation, though the differences at the microscopic level have non-trivial consequences. To point them out, we investigate an extension of these dynamics in which confidence/trust is considered, focusing on the case of an underlying fully connected graph, and we show that the consensus-polarization phase transition taking place in the Naming Game is not observed in the AB model. We then consider the interface motion in regular lattices. Qualitatively, both models show the same behavior: a diffusive interface motion in a one-dimensional lattice, and a curvature driven dynamics with diffusing stripe-like metastable states in a two-dimensional one. However, in comparison to the Naming Game, the AB-model dynamics is shown to slow down the diffusion of such configurations.


64.60.Cn Order-disorder transformations 87.23.Ge Dynamics of social systems 


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.IFISC, Institut de Física Interdisciplinària i Sistemes Complexos (CSIC-UIB), Campus Universitat Illes BalearsPalma de MallorcaSpain
  2. 2.Departament de Física i Enginyeria NuclearUniversitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Dipartimento di Fisica“Sapienza” Università di RomaRomaItaly
  4. 4.Fondazione ISITorinoItaly

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