论文标题
高于上部临界维度上方多数票数模型的有限尺寸缩放
Finite-Size Scaling of the majority-voter model above the upper critical dimension
论文作者
论文摘要
多数投票模型通过蒙特卡洛模拟在尺寸的高素质晶格上进行了研究，$ d = 2 $至7，并在周期性边界条件下进行。与磁敏感性的有限尺寸缩放相关的临界指数与Ising模型的尺寸缩放率相兼容。在尺寸$ d = 4 $时，数值数据与乘法对数校正的存在兼容。对于$ d \ ge 5 $，当考虑到Gaussian固定点的危险无关变量时，指数的估计值接近预测$ d/2 $。此外，粘合剂累积剂的通用值也与Ising模型的通用值兼容。这表明大多数投票器模型的上部临界维度不是$ d_c = 6 $，如文献所述，而是$ d_c = 4 $，例如equilibrium ising模型。
The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension $d=2$ to 7 with periodic boundary conditions. The critical exponents associated to 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 are close to the prediction $d/2$ when taking into account the dangerous irrelevant variable at theGaussian fixed point. 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.
