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Multistate voter model with imperfect copying.

Federico Vazquez1, Ernesto S Loscar2, Gabriel Baglietto2

  • 1Instituto de Cálculo, FCEN, Universidad de Buenos Aires and CONICET, Buenos Aires, Argentina.

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Summary
This summary is machine-generated.

Introducing a noisy multistate voter model, this study reveals that copying errors disrupt population ordering. Complete order is lost as population size increases, even with slight imperfections.

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Area of Science:

  • Statistical Physics
  • Complex Systems Modeling

Background:

  • The multistate voter model is widely used in fields like population genetics and opinion dynamics.
  • The basic model assumes perfect state copying between individuals.

Purpose of the Study:

  • To investigate a variant of the multistate voter model with imperfect copying (noise).
  • To analyze how copying error amplitude and population size affect ordering properties.

Main Methods:

  • Mean-field analysis of the noisy multistate voter model.
  • Monte Carlo simulations to validate theoretical findings.

Main Results:

  • Perfect copying (η=0) leads to complete order (ψ=1) regardless of population size.
  • Any copying imperfection (η>0) causes ordering to decrease with population size (N).
  • The average order parameter 〈ψ〉 scales as 1/(η^2 N) for small errors and large populations.

Conclusions:

  • The multistate noisy voter model loses complete order in the thermodynamic limit (N→∞).
  • Even small amounts of noise prevent the system from reaching perfect order.
  • The model provides a minimalistic framework for understanding flocking dynamics with noise.