Ordering kinetics of the two-dimensional voter model with long-range interactions

Area of Science:

• Statistical Physics
• Complex Systems
• Agent-Based Modeling

Background:

• The voter model is a fundamental tool for studying opinion dynamics and social influence.
• Understanding how interaction range affects ordering kinetics is crucial for realistic modeling.

Purpose of the Study:

• To analytically investigate the ordering kinetics of the two-dimensional long-range voter model.
• To characterize different dynamical regimes based on the interaction exponent α.
• To analyze domain growth, consensus times, and scaling behavior.

Main Methods:

• Analytical study of the voter model on a 2D lattice.
• Analysis of opinion dynamics with long-range interactions P(r)∝r^{-α}.
• Investigation of different regimes for α>4 and 0<α≤4.

Main Results:

• For α>4, behavior resembles nearest-neighbor models with L(t)∝sqrt[t] growth and NlnN consensus time, but with violated scaling.
• For 0<α≤4, standard scaling L(t)∝t^{1/z} is observed, with 1/z dependent on α.
• Systems with α≤3 reach a metastable state, with consensus in finite systems occurring in O(N) time.

Conclusions:

• The interaction range significantly alters ordering kinetics and scaling behavior in the 2D voter model.
• Distinct regimes exist for α>4 and 0<α≤4, impacting domain growth and consensus.
• Long-range interactions can lead to metastable states and modified consensus dynamics.