AI 中文总结
研究通过结合共形映射与单应变换对三维伊辛模型的七圈和八圈重整化群级数重新求和来确定临界指数，给出精确估计及不确定性估计，发现 $\eta$ 误差条随圈阶数快速减小，与共形引导估计有紧张关系并探讨其影响。
AI 中文摘要
我们通过对最近计算的在 $\epsilon = 4 - d$ 展开中的七圈和八圈重整化群级数进行重新求和，来确定三维伊辛普适类的临界指数 $\eta$、$\nu$ 和标度修正指数 $\omega$。重新求和将共形映射与单应变换相结合，同时根据两个互补标准优化重新求和参数。该方法能给出临界指数的精确估计以及定量的不确定性估计。我们发现 $\eta$ 的误差条随着圈阶数增加迅速减小，而 $\nu$ 和 $\omega$ 并非如此。出乎意料的是，尽管估计值在绝对值上是准确，但它们与圈阶数的缓慢收敛导致与目前被视为基准的共形引导估计存在轻微但系统的紧张关系。我们讨论了这种行为的几个可能起源及其对微扰重整化群级数高阶重新求和的影响。
英文摘要
We determine the critical exponents $η$, $ν$, and the correction-to-scaling exponent $ω$ of the three-dimensional Ising universality class by resumming the recently computed seven- and eight-loop renormalization-group series in the $ε=4-d$ expansion (O.~Schnetz, \textit{Phys. Rev. D} \textbf{97}, 085018 (2018); O.~Schnetz, \textit{Phys. Rev. D} \textbf{107}, 036002 (2023)). The resummation combines conformal mapping with a homographic transformation, while the resummation parameters are optimized according to two complementary criteria. This approach yields precise estimates of the critical exponents together with quantitative uncertainty estimates. We find that the error bar on $η$ decreases rapidly with increasing loop order, whereas this is the case neither for $ν$ nor for $ω$. Unexpectedly, although the estimated values are accurate in absolute terms, their slow convergence with the loop order leads to a slight but systematic tension with the conformal bootstrap estimates that are currently considered as the benchmark. We discuss several possible origins of this behavior and its implications for high-order resummations of perturbative renormalization-group series.
Comments36 pages, 19 figures, 6 tables
