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Three-state majority-vote model on a simple cubic lattice.

Wooseop Kwak1, Jae Hwan Lee2, Jin Min Kim2

  • 1Chosun University, Department of Integrated Mathematical Science, Gwangju 61452, Korea.

Physical Review. E
|May 16, 2026
PubMed
Summary
This summary is machine-generated.

The three-state majority-vote model on a cubic lattice exhibits a weak first-order phase transition. Monte Carlo simulations revealed critical behavior consistent with this transition, confirmed by magnetization and susceptibility analyses.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems

Background:

  • The majority-vote model is a fundamental tool for studying opinion dynamics and phase transitions in systems with discrete states.
  • Understanding phase transitions in lattice models is crucial for fields ranging from physics to social sciences.

Purpose of the Study:

  • To investigate the phase transition dynamics of the three-state majority-vote model on a simple cubic lattice.
  • To characterize the nature of the phase transition using key thermodynamic quantities and critical exponents.

Main Methods:

  • Monte Carlo simulations were employed to model the system's dynamics.
  • Magnetization, magnetic susceptibility, and Binder cumulant were monitored to analyze critical phenomena.
  • Scaling analysis was performed on simulation data to determine critical exponents.

Main Results:

  • The magnetization exhibited a rapid change near the critical noise parameter (q_c), indicating a phase transition.
  • Analysis of magnetic susceptibility yielded a critical exponent ratio γ/ν ≈ 2.91, suggesting a weak first-order transition.
  • The Binder cumulant showed a pronounced negative dip near q_c for large system sizes, providing further evidence for the transition type.

Conclusions:

  • The three-state majority-vote model on a simple cubic lattice undergoes a weak first-order phase transition.
  • The obtained critical exponent ratio and Binder cumulant behavior are consistent with theoretical predictions for such transitions.