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Condensed Matter > Statistical Mechanics
Title: Finite-Size Scaling of the majority-voter model above the upper critical dimension
(Submitted on 2 Nov 2022 (this version), latest version 6 Jan 2023 (v2))
Abstract: 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.
Submission history
From: Christophe Chatelain [view email][v1] Wed, 2 Nov 2022 10:00:16 GMT (61kb)
[v2] Fri, 6 Jan 2023 12:12:13 GMT (55kb)
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