Algebraic coarsening in voter models with intermediate states

2008/06/05 by Luca Dall'Asta, Luca Dall’Asta, Tobias Galla · 32 citations
Mathematics · Physics and Astronomy · #Algebraic number #Applied mathematics #Computer science #Dynamics (music) #Langevin equation #Lattice (music) #Logarithm #Mathematical analysis #Mathematics #Multiplicative function #Multiplicative noise #Opinion Dynamics and Social Influence #Physics #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Voter model #cond-mat.stat-mech #physics.soc-ph

paper · pdf · doi:10.1088/1751-8113/41/43/435003

published in Journal of Physics A Mathematical and Theoretical 41(43), 435003 (Institute of Physics) · 11 pages, 5 figures; minor typos corrected

arxiv created 2008/06/05 · openalex publication_date 2008/09/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The introduction of intermediate states in the dynamics of the voter model modifies the ordering process and restores an effective surface tension. The logarithmic coarsening of the conventional voter model in two dimensions is eliminated in favour of an algebraic decay of the density of interfaces with time, compatible with Model A dynamics at low temperatures. This phenomenon is addressed by deriving Langevin equations for the dynamics of appropriately defined continuous fields. These equations are analyzed using field theoretical arguments and by means of a recently proposed numerical technique for the integration of stochastic equations with multiplicative noise. We find good agreement with lattice simulations of the microscopic model.

Citations

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