Antiferromagnetic majority voter model on square and honeycomb lattices

TL;DR

This study introduces an antiferromagnetic majority voter model on square and honeycomb lattices, demonstrating a continuous phase transition and universality class alignment with the Ising model through Monte Carlo simulations.

Contribution

It presents the first analysis of an antiferromagnetic majority voter model, including critical points and exponents, expanding understanding of voter models in statistical physics.

Findings

Evidence of continuous phase transition in both lattices

Critical exponents match Ising universality class

Critical points estimated with high precision

Abstract

An antiferromagnetic version of the well-known majority voter model on square and honeycomb lattices is proposed. Monte Carlo simulations give evidence for a continuous order-disorder phase transition in the stationary state in both cases. Precise estimates of the critical point are found from the combination of three cumulants, and our results are in good agreement with the reported values of the equivalent ferromagnetic systems. The critical exponents $1/\nu$, $\gamma/\nu$ and $\beta/\nu$ were found. Their values indicate that the stationary state of the antiferromagnetic majority voter model belongs to the Ising model universality class.