AI 中文总结
该研究针对O(N)不变ϕ⁴模型，将全超几何重求和算法应用于七圈ε级数，证实大N下临界指数估计精度提升，其误差与蒙特卡罗等方法相当。
AI 中文摘要
近年来，对临界状态下O(N)对称模型的大N情况的研究受到了广泛关注。特别是，一项最新的高精度蒙特卡罗研究（《物理评论B》105, 054428 (2022)）给出了N≥4时临界指数ν、η和ω迄今最精确的估计值。在重整化群（RG，现代临界现象理论的基石）框架内，存在ε展开和非微扰RG等强大的计算方法。由于ε展开中的有效展开参数σ=3/(N+8)随N增大而减小，人们预期重求和技术在大N regime中会变得越来越精确。为验证这一预期，我们将Shalaby等人开发的全超几何重求和算法应用于最近获得的N≥4时的七圈发散ε级数，得到了ν、η和ω的高精度估计值。我们的分析证实了精度随N增大而提升的预期。为评估这些结果的重要性，我们注意到，在相同的七圈阶下，O(2)情况的误差比实验、蒙特卡罗模拟和共形场论分析得到的误差大一个数量级。相比之下，对于足够大的N，本工作中的误差与蒙特卡罗和非微扰RG方法的误差处于同一数量级，证明了我们的重求和方法在大N regime中的强大预测能力。
英文摘要
The study of large-$N$ cases of the $O(N)$-symmetric model at criticality has attracted significant attention in recent years. In particular, a recent high-precision Monte Carlo study ( Physical Review B 105, 054428 (2022)) reported the most accurate estimates to date for the critical exponents $ν$, $η$, and $ω$ for $N \ge4$. Within the framework of the renormalization group (RG)---the cornerstone of the modern theory of critical phenomena---powerful computational approaches such as the $\varepsilon$-expansion and non-perturbative RG are available. Since the effective expansion parameter in the $\varepsilon$-expansion, $σ= \frac{3}{N+8}$, decreases with increasing N, one expects resummation techniques to become progressively more accurate in the large-N regime. To test this expectation, we apply the entire-hypergeometric resummation algorithm developed by Shalaby et al. to the recently obtained seven-loop divergent $\varepsilon$-series for $N \ge 4$, yielding high-precision estimates for $ν$, $η$, and $ω$ . Our analysis confirms the anticipated improvement in accuracy with increasing N. To assess the significance of these results, we note that at the same seven-loop order the $O(2)$ case exhibits errors that are an order of magnitude larger than those obtained from experiment, Monte Carlo simulations, and conformal-field-theory analysis. In contrast, for sufficiently large N, the errors in the present work are of the same order of magnitude as those from Monte Carlo and non-perturbative RG methods, demonstrating the strong predictive power of our resummation approach in the large-N regime.
Comments17 pages, 1 figure
