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Percolation in a kinetic opinion exchange model.

Anjan Kumar Chandra1

  • 1Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India. anjanphys@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 3, 2012
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Summary

This study explores geometrical cluster percolation in the LCCC opinion model. The critical exponents for this percolation transition are robust and indicate a unique universality class, distinct from other known models.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Computational Physics

Background:

  • The LCCC model is a kinetic opinion exchange model on a square lattice.
  • Understanding opinion dynamics and phase transitions is crucial in complex systems.

Purpose of the Study:

  • Investigate the percolation transition of geometrical clusters in the LCCC model.
  • Determine if the critical exponents belong to a known universality class.

Main Methods:

  • Simulated the LCCC model on a square lattice.
  • Defined clusters based on opinion values exceeding a threshold (Ω).
  • Analyzed critical exponents using data collapses of cluster size and Binder cumulant.

Main Results:

  • Identified a percolation transition for geometrical clusters, distinct from the order parameter transition.
  • Found that critical exponents are independent of conviction and influencing parameters.
  • Observed that the exponents do not match those of static Ising, dynamic Ising, or standard percolation.

Conclusions:

  • The LCCC model's geometrical cluster percolation belongs to a unique universality class.
  • The percolation transition is robust across different parameter values.
  • This finding contributes to the classification of universality classes in opinion dynamics models.