2004/12/31 by Mauro Mobilia, Ivan T. Georgiev · 3 citations
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1103/physreve.71.046102
published as Phys. Rev. E 71, 046102 (2005) · 17 pages, 6 figures, revtex4 2-column format. Original title ("Are Voting and Catalytic Processes Electrostatic Problems ?") changed upon editorial request. Minor typos corrected. Published in Physical Review E
openalex publication_date 2005/04/01 · arxiv created 2005/04/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the dynamics of the voter model and of the monomer-monomer catalytic process in the presence of many "competing" inhomogeneities and show, through exact calculations and numerical simulations, that their presence results in a non-trivial fluctuating steady state whose properties are studied and turn out to specifically depend on the dimensionality of the system, the strength of the inhomogeneities, and their separating distances. In fact, in arbitrary dimensions, we obtain an exact (yet formal) expression of the order parameters (magnetization and concentration of adsorbed particles) in the presence of an arbitrary number n of inhomogeneities ("zealots" in the voter language) and formal similarities with suitable electrostatic systems are pointed out. In the non-trivial cases n = 1,2, we explicitly compute the static and long-time properties of the order parameters and therefore capture the generic features of the systems. When n > 2 , the problems are studied through numerical simulations. In one spatial dimension, we also compute the expressions of the stationary order parameters in the completely disordered case, where n is arbitrary large. Particular attention is paid to the spatial dependence of the stationary order parameters and formal connections with electrostatics.