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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

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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Dates et versions

hal-03834847 , version 1 (31-10-2022)
hal-03834847 , version 2 (06-01-2023)

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Christophe Chatelain. Finite-Size Scaling of the majority-voter model above the upper critical dimension. 2022. ⟨hal-03834847v1⟩
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