1 research outputs found
Consensus and ordering in language dynamics
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.Comment: 7 pages, 6 figure