在大N极限下，从O(N)对称场论中ε展开的最优截断精确提取临界指数
Accurate Critical Exponents from the Optimal Truncation of the epsilon- Expansion within the O(N)-symmetric Field Theory for large N
AI总结：
本文证明在O(N)对称ϕ^4场论中，对于N≥4，利用最优截断的ε展开部分和及七阶Padé近似可精确计算临界指数ν、η和ω，结果与蒙特卡洛和共形场计算相当，且大N极限与非微扰1/N展开一致。
摘要：
O(N)对称的ϕ^4场论的重整化群函数的微扰级数是发散的，但具有渐近性质。通常需要对其进行重求和计算以提取可靠结果。尽管QED级数也具有相同的特征，但由于微扰参数很小，其部分和可以返回精确结果。然而，在本工作中，我们表明，对于N≥4，指数ν和η的级数部分和（根据最优截断）给出的结果与最近的蒙特卡洛和共形场计算具有很强的竞争力。该级数可以用微扰参数α=σε=3/(N+8)ε表示，该参数在N较大时更小，因此随着N增大，人们期望像QED情形一样获得精确的微扰结果。然而，这种最优截断对于临界指数ω的级数（对于中等N值）并不适用，因为截断后的级数只包含一阶项。尽管如此，对于N≥4，大阶参数σ=3/(N+8)变得越来越小，这为使用Padé近似提供了合理性。为此，我们首先从最近可用的相应g展开中获得了七阶ε级数。七阶Padé近似对这三个指数给出了精确结果。此外，对于级数中的所有七个阶，大N极限都得到了由非微扰1/N展开所预言的精确结果。
英文摘要：
The perturbation series for the renormalization group functions of the $O(N)-$symmetric $ϕ^4$ field theory are divergent but asymptotic. They are usually followed by Resummation calculations to extract reliable results. Although the same features exist for QED series, their partial sums can return accurate results because the perturbation parameter is small. In this work, however, we show that, for $N\ge4$, the partial sum ( according to optimal truncation) of the series for the exponents $ν$ and $η$ gives results that are very competitive to the recent Monte Carlo and Conformal field calculations. The series can be written in terms of the perturbation parameter $α=σ\varepsilon=\frac{3}{N+8}\varepsilon$ which is smaller for larger $N$ and thus as $N$ increases one expects accurate perturbative results like the QED case. Such optimal truncation, however, doesn't work for the series of the critical exponent $ω$ ( for intermediate values of $N$) as the truncated series includes only the first order. Nevertheless, for $N\ge4$, the large-order parameter $σ=\frac{3}{N+8}$ is getting smaller which rationalizes for the use of the Pad$\acute{e}$ approximation. For that aim, we first obtain the seven-loop $\varepsilon$-series from the recent available corresponding $g$-expansion. The seven-loop Pad$\acute{e}$ approximation gives accurate results for the three exponents. Besides, for all the seven orders in the series, the large-$N$ limit leads to the exact result predicted by the non-perturbative $1/N$-Expansion.
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