Exact solution of the isotropic majority-vote model on complete graphs.

Area of Science:

• Statistical Mechanics
• Complex Systems

Background:

• The isotropic majority-vote (MV) model is often considered a nonequilibrium model that violates detailed balance, except in one dimension.
• Understanding the equilibrium properties of such models is crucial for statistical mechanics and complex systems research.

Purpose of the Study:

• To investigate the detailed balance condition of the MV model when defined on a complete graph.
• To determine the equilibrium properties and stationary distribution of the MV model on a fully connected graph.

Main Methods:

• Analysis of the MV model on a complete graph using the master equation approach.
• Derivation of the exact probability distribution for spin configurations.
• Comparison with the modified Ehrenfest urn model.

Main Results:

• The MV model on a complete graph fulfills the detailed balance condition in the stationary regime.
• The model is shown to be equivalent to the modified Ehrenfest urn model.
• The derived probability distribution depends solely on the absolute value of magnetization.

Conclusions:

• The common assumption about the MV model violating detailed balance does not hold for complete graphs.
• The MV model on a complete graph represents an equilibrium system with a unique probability distribution.
• Theoretical predictions are confirmed through numerical simulations, validating the findings.