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The HoneyComb Paradigm for Research on Collective Human Behavior
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Published on: January 19, 2019

Effective multidimensional crossover behavior in a one-dimensional voter model with long-range probabilistic

D E Rodriguez1, M A Bab, E V Albano

  • 1Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CCT-La Plata CONICET, La Plata, Argentina. rodrigdiego@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 17, 2011
PubMed
Summary

This study introduces a voter model variant with long-range interactions, finding that the interaction range (σ) dictates dynamics. Ordering is lost for σ<1, while ordering emerges for σ>1, with critical behavior near σ≈1.

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Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • The standard voter model simulates opinion dynamics on lattices.
  • Nearest-neighbor interactions are typical, but long-range effects are less understood.

Purpose of the Study:

  • To investigate how long-range interactions influence the voter model dynamics.
  • To analyze the crossover behavior induced by varying interaction range parameter σ.

Main Methods:

  • Numerical simulations on a one-dimensional lattice.
  • Dynamical and finite-size scaling arguments.
  • Analysis of interaction probability P(r)∝r(-(d+σ)).

Main Results:

  • For σ<1, ordering is lost, showing steady-state or exponential decay in finite systems.
  • For σ>1, ordering dynamics emerge, with exponent α depending on σ.
  • Critical-type behavior observed at σ≈1, analogous to the standard voter model's critical dimension.

Conclusions:

  • The voter model's dynamics are highly sensitive to interaction range.
  • Long-range interactions introduce effective multidimensional crossover behavior.
  • The parameter σ controls the transition between different dynamic regimes.