二维格点O（N）模型中截断效应的大幅度减少
Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models
摘要：
我们调查的截止效应在2-D晶格O（N）模型的各种晶格行动，我们确定了一类非常简单的行动，晶格文物是非常小的。一个动作与标准动作一致，除了它将相邻的自旋限制在最大相对角度δ。我们通过要求阶跃标度函数的特定值与已经在相当粗糙的晶格上的连续结果一致来固定δ。值得注意的是，整个阶跃标度函数的截止效应然后降低到千分之一的水平。这也适用于2-d O（3）模型中阶跃标度函数的θ真空效应。其他物理观测量的截止效应，包括重整化耦合和质量在等张量通道也大大减少。另一种选择是混合作用量，它将标准二次项与适当调整的大四次项结合起来，也具有极小的截止效应。截断效应的大小也进行了研究分析，在1-D和在N =无穷大的2-D。
英文摘要：
We investigate the cutoff effects in 2-d lattice O(N) models for a variety of lattice actions, and we identify a class of very simple actions for which the lattice artifacts are extremely small. One action agrees with the standard action, except that it constrains neighboring spins to a maximal relative angle delta. We fix delta by demanding that a particular value of the step scaling function agrees with its continuum result already on a rather coarse lattice. Remarkably, the cutoff effects of the entire step scaling function are then reduced to the per mille level. This also applies to the theta-vacuum effects of the step scaling function in the 2-d O(3) model. The cutoff effects of other physical observables including the renormalized coupling and the mass in the isotensor channel are also reduced drastically. Another choice, the mixed action, which combines the standard quadratic with an appropriately tuned large quartic term, also has extremely small cutoff effects. The size of cutoff effects is also investigated analytically in 1-d and at N = infinity in 2-d.
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