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J Toruniewska1, K Kułakowski2, K Suchecki1

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In the coevolving voter model, researchers found that in the active phase, node and link magnetizations equalize. Above a critical rewiring probability, the system freezes, leading to different magnetization values.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Network Science

Background:

  • The voter model is a fundamental tool for studying opinion dynamics on networks.
  • Coevolutionary models, where network structure and node states influence each other, offer richer insights into real-world systems.
  • Understanding phase transitions in dynamic networks is crucial for predicting system behavior.

Purpose of the Study:

  • To investigate the final state dynamics of the coevolving voter model.
  • To analyze the interplay between state copying and link rewiring in determining system behavior.
  • To identify and characterize the absorbing transition to a frozen phase.

Main Methods:

  • Analytical calculations and numerical simulations were employed.
  • The study focused on the behavior of magnetization and node degrees.
  • A statistical conservation law was derived and analyzed.

Main Results:

  • In the active phase, mean node and link magnetizations converge to the same value, dependent on initial conditions.
  • A statistical conservation law, Λ≡(1-p)μm(t)+pn(t)=const., governs the system's evolution.
  • Above the critical rewiring probability, the system enters a frozen phase with distinct node and link magnetizations and potentially unequal spin degrees.

Conclusions:

  • The coevolving voter model exhibits a critical transition to a frozen phase.
  • The system's final state in the active phase is characterized by emergent equalities in magnetization and spin degrees, governed by a conservation law.
  • Network topology changes significantly impact the dynamics and final states, especially in the frozen phase.