Tunable disorder on the S-state majority-voter model.

Area of Science:

• Statistical Physics
• Complex Systems

Background:

• Investigating nonequilibrium phase transitions is crucial for understanding complex systems.
• The S-state majority-vote model provides a framework for studying collective behavior with local interactions.

Purpose of the Study:

• To analyze the nonequilibrium phase transition in the S-state majority-vote model for S=2, 3, and 4.
• To determine the influence of a hyperbolic distribution of noise thresholds on system disorder.
• To characterize the critical behavior and exponents of the phase transition.

Main Methods:

• Utilizing Monte Carlo simulations on regular square lattices.
• Employing finite-size scaling analyses to deduce critical phenomena.
• Analyzing the relationship between the critical threshold and the number of nearest neighbors (Nv).

Main Results:

• A continuous order-disorder phase transition was identified at a critical parameter αc.
• The critical threshold (αc) shows a power-law decay with respect to Nv (αc∼Nv-δ).
• The calculated critical exponents (β/ν and γ/ν) align with those of the S-state Potts model.

Conclusions:

• The S-state majority-vote model exhibits a continuous phase transition driven by varying noise thresholds.
• The system's critical behavior is dependent on the number of neighbors, following a power-law relationship.
• The model's critical exponents suggest a connection to the universality class of the S-state Potts model.