AI 中文总结
研究精确（泛函）重整化群导数展开在各维度下的渐近行为，通过无质量λφ⁴微扰理论证明其发散，经多理论论证及分析两圈和三圈贡献，得出其为渐近级数，先收敛后发散的结论。
AI 中文摘要
我们表明，精确（泛函）重整化群的导数展开在任何维度下都是一个发散级数，无论是对于指数截断还是更一般的光滑截断。我们通过在无质量的λφ⁴微扰理论中证明这种发散首先出现在两圈来证实这一点。通过几条理论论证线并分析两圈和三圈贡献的无限类，我们得出导数展开是一个渐近级数，它在发散行为占主导之前最初会收敛到精确结果。
英文摘要
We show that the derivative expansion of the exact (functional) renormalization group is a divergent series in any dimension, both for an exponential cutoff and more general smooth cutoffs. We prove this by showing that within massless $λφ^4$ perturbation theory, such divergences arise first at two loops. From several lines of theoretical argument and by analysing infinite classes of two- and three-loop contributions, we conclude that the derivative expansion is an asymptotic series that initially converges towards the exact result before divergent behaviour takes over.
Comments50 pages
