论文标题
来自非扰动重新归如此的$ O（N）$模型的关键指数的分析性
Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization
论文作者
论文摘要
我们在衍生产品扩展中采用二阶功能性重归其化组框架来研究$ o（n）$模型，以不断改变现场组件$ n $和空间维度$ d $。在$（d，n）$平面中的一条线上，我们特别解决了有关关键指数$ν$和$η$的非分析行为的Cardy-Hamber预测，该预测通过了点$（2,2）$。通过$η（d，n）$和$ν{ - 1}（d，n）$的直接数值评估，以及对功能固定点配置文件的分析，我们以$（d，n）$平面中的两个方案之间的交叉形式清楚地指示了这一行的形式，但是，这些$（d，n）$平面的证据，但是没有不连续的或sikular first和sickular first和section section derivitions $ d $ d $ d $ d $ d $ d $ d $ d $ d = dd = d d $ d dd> d $ d = dd = d of。 $η（d，n）$和$ν{ - 1}（d，n）$的计算衍生物对于$ d \ to 2 $ to 2 $和$ n \ to 2 $变得越来越大，只有在此限制中，$η（d，n）$和$ν$和$ν^{-1}（-1}（-1}（d，n）$ as a g y US yous yous vent Ivernynannanaly nonananalyallynanalyally nonananalyalyally nonanalyalaly ys nonananalyalyalyalyalyalyallyallyally ys nonanalyalaly。通过扫描RG转换的二级特征值的依赖性$ n $，对于$ d> 2 $，我们没有发现其消失的迹象，正如Cardy-Hamber场景所预期的那样。对于$ d $接近3的维度，即使是跨界界的签名，也没有签名，即以预期形式的非分析性形式的交叉及其存在。
We employ the functional renormalization group framework at the second order in the derivative expansion to study the $O(N)$ models continuously varying the number of field components $N$ and the spatial dimensionality $d$. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents $ν$ and $η$ across a line in the $(d,N)$ plane, which passes through the point $(2,2)$. By direct numerical evaluation of $η(d,N)$ and $ν^{-1}(d,N)$ as well as analysis of the functional fixed-point profiles, we find clear indications of this line in the form of a crossover between two regimes in the $(d,N)$ plane, however no evidence of discontinuous or singular first and second derivatives of these functions for $d>2$. The computed derivatives of $η(d,N)$ and $ν^{-1}(d,N)$ become increasingly large for $d\to 2$ and $N\to 2$ and it is only in this limit that $η(d,N)$ and $ν^{-1}(d,N)$ as obtained by us are evidently nonanalytical. By scanning the dependence of the subleading eigenvalue of the RG transformation on $N$ for $d>2$ we find no indication of its vanishing as anticipated by the Cardy-Hamber scenario. For dimensionality $d$ approaching 3 there are no signatures of the Cardy-Hamber line even as a crossover and its existence in the form of a nonanalyticity of the anticipated form is excluded.
