论文标题
通过O（n）群岛导航
Navigating through the O(N) archipelago
论文作者
论文摘要
最近在ARXIV中提出了一种在CFT数据空间（CFT-DATA）（CFT-DATA）空间中的区域的新方法，该方法在ARXIV：2104.09518中提出。在最简单的示例中，即3D ISING模型的混合相关研究的功效证明了其功效。在本文中，我们想证明，导航器方法也可以应用于$ d $二维$ o（n）$型号的家族的研究。我们的目标是在$（d，n）$平面中遵循这些模型。我们将看到，从岛到岛的“航行”可以在导航器的背景下被理解为参数优化问题，我们将利用这一事实来实施一种简单有效的路径遵循算法。通过与$（d，n）$平面一起航行，我们将在整个范围$（d，n）\ in [3,4] \ times [1,3] $中提供缩放尺寸$（δ_2，δ__{s}，δ__{s}，δ__{t}）$。我们将表明，由于该范围内的$ d $或$ n $的分数值，因此我们无法看到$ O（N）$模型的非独立性。我们还将研究限制$ n \ xrightArrow [] {} 1 $，并且看到我们找不到对低于$ n = 1 $的单一混合相关跨方程的任何解决方案。
A novel method for finding allowed regions in the space of CFT-data, coined navigator method, was recently proposed in arXiv:2104.09518. Its efficacy was demonstrated in the simplest example possible, i.e. that of the mixed-correlator study of the 3D Ising Model. In this paper, we would like to show that the navigator method may also be applied to the study of the family of $d$-dimensional $O(N)$ models. We will aim to follow these models in the $(d,N)$ plane. We will see that the "sailing" from island to island can be understood in the context of the navigator as a parametric optimization problem, and we will exploit this fact to implement a simple and effective path-following algorithm. By sailing with the navigator through the $(d,N)$ plane, we will provide estimates of the scaling dimensions $(Δ_ϕ,Δ_{s},Δ_{t})$ in the entire range $(d,N) \in [3,4] \times [1,3]$. We will show that to our level of precision, we cannot see the non-unitary nature of the $O(N)$ models due to the fractional values of $d$ or $N$ in this range. We will also study the limit $N \xrightarrow[]{} 1$, and see that we cannot find any solution to the unitary mixed-correlator crossing equations below $N=1$.
