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Majority versus minority dynamics: phase transition in an interacting two-state spin system.
1Center for BioDynamics, Center for Polymer Studies & Department of Physics, Boston University, Boston, Massachusetts 02215, USA. mmobilia@bu.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
Summary
This study models opinion dynamics where agents adopt majority or minority states. A phase transition occurs at p(c)=2/3, leading to either global majority rule or a mixed state, with conserved magnetization at the critical point.
Area of Science:
- Statistical physics
- Complex systems
Background:
- Opinion dynamics models explore how collective beliefs emerge.
- Local interactions significantly influence system-wide behavior.
Purpose of the Study:
- To introduce and analyze a novel opinion dynamics model.
- To investigate the impact of local majority/minority influence on opinion formation.
Main Methods:
- Agent-based modeling with binary-state agents.
- Analysis of phase transitions and critical phenomena.
- Application of Kirkwood decoupling scheme in one dimension.
Main Results:
- A phase transition at p(c)=2/3 for group size G=3 across spatial dimensions.
- For p>p(c), global majority state prevails; for p
- At p(c), magnetization is conserved, and dynamics resemble the classical voter model.
Conclusions:
- The model exhibits distinct macroscopic behaviors based on the probability p.
- System dynamics at the critical point align with established voter model behaviors.
- Finite-length systems show non-trivial magnetization dependence on initial conditions near p(c).