Finite-Size Scaling of the majority-voter model above the upper critical dimension
Résumé
The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices
of dimension $d=2$ to 7. The critical exponents $\gamma/\nu$ estimated from the
Finite-Size Scaling of the magnetic susceptibility are shown to be compatible with
those of the Ising model. At dimension $d=4$, the numerical data are compatible with
the presence of multiplicative logarithmic corrections. For $d\ge 5$, the estimates
of the exponents $\gamma/\nu$ are close to the prediction $\gamma/\nu=d/2$ of the
$\phi^4$ theory above the upper critical dimension. Moreover, the universal values
of the Binder cumulant are also compatible with those of the Ising model.
This indicates that the upper critical dimension of the majority-voter model
is not $d_c=6$ as claimed in the literature, but $d_c=4$ like the equilibrium
Ising model.
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