Antiferromagnetic majority voter model on square and honeycomb lattices

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 $1/ν$, $γ/ν$ and $β/ν$ were found. Their values indicate that the stationary state of the antiferromagnetic majority voter model belongs to the Ising model universality class.

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