论文标题
3d $ O（n）$矢量模型中相图的自由度和翻新依赖性
Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models
论文作者
论文摘要
在经典阶段，3d $ o（n）$对称$ ϕ^4 $ vector模型接纳了与Chang和Magruder很久以前发现的强度型二元相关的两个等效描述。我们确定弱分支和强大分支中临界耦合的确切分析性重新规范化依赖性是重新归一化方案（通过$κ$）和任何$ n $的函数的函数。结果表明，对于$κ=κ_*$，两个固定点合并，然后，对于$κ<κ_*$，它们以复杂的共轭配对进入复杂的平面，从而使相变不再从经典的毫无损失的阶段看到。 $ n = 1 $ $ ϕ^4 $理论适用于2D，其中经典破碎和不间断的阶段的作用被倒置。我们通过计算真空能量的3D $ O（n）$模型的扰动系列来验证所有这些考虑因素，并使大量差距达到第8阶，并且Borel重新定位了该系列。特别是，我们提供了自我双重性的数值证据，并验证在重新归一化方案中，临界耦合很复杂的理论被掩盖了。作为我们分析的副产品，我们展示了如何将2D中$ n $的非扰动质量差距视为在经典不间断的阶段的扰动的分析延续。
In the classically unbroken phase, 3d $O(N)$ symmetric $ϕ^4$ vector models admit two equivalent descriptions connected by a strong-weak duality closely related to the one found by Chang and Magruder long ago. We determine the exact analytic renormalization dependence of the critical couplings in the weak and strong branches as a function of the renormalization scheme (parametrized by $κ$) and for any $N$. It is shown that for $κ=κ_*$ the two fixed points merge and then, for $κ<κ_*$, they move into the complex plane in complex conjugate pairs, making the phase transition no longer visible from the classically unbroken phase. Similar considerations apply in 2d for the $N=1$ $ϕ^4$ theory, where the role of classically broken and unbroken phases is inverted. We verify all these considerations by computing the perturbative series of the 3d $O(N)$ models for the vacuum energy and for the mass gap up to order eight, and Borel resumming the series. In particular, we provide numerical evidence for the self-duality and verify that in renormalization schemes where the critical couplings are complex the theory is gapped. As a by-product of our analysis, we show how the non-perturbative mass gap at large $N$ in 2d can be seen as the analytic continuation of the perturbative one in the classically unbroken phase.
