O（N）对称量子场模型临界指数的超几何Meijer求和
Precise Critical Exponents of the O(N)-Symmetric Quantum field Model using Hypergeometric-Meijer Resummation
摘要：
在这项工作中，我们表明，可以选择不同类型的超几何逼近的重新表示的发散级数与不同的大阶增长因子。由于具有$n!$增长因子，本文用超几何函数$_{k+1}F_{k-1}$逼近$O(N)$对称模型临界指数的$\varepsilon$展开式的发散级数.发散的$_{k+1}F_{k-1}$功能，然后使用其等效的Meijer-G函数表示。指数$ν$、\ $η$和$ω$的重新计算结果的收敛性已被证明在从低阶到最高已知六环阶的过程中系统地改善。我们的六圈remation结果是非常有竞争力的最近的六圈Borel与保角映射预测和最近的Monte Carlo模拟结果。为了表明精确结果适用于高$N$值，我们列出了$ν$的五个循环结果，这些结果也非常精确。本文还计算了重整化群函数$β,γ_{ϕ^2}$和$γ_{m^2}$的最近的七圈序（$g$ -级数）。从$β$、$γ_{ϕ^2}$和$γ_{m^2}$近似式中提取了临界耦合和指数$ν$、$η$和$ω$的精确预测。
英文摘要：
In this work, we show that one can select different types of Hypergeometric approximants for the resummation of divergent series with different large-order growth factors. Being of $n!$ growth factor, the divergent series for the $\varepsilon$-expansion of the critical exponents of the $O(N)$-symmetric model is approximated by the Hypergeometric functions $_{k+1}F_{k-1}$. The divergent $_{k+1}F_{k-1}$ functions are then resummed using their equivalent Meijer-G function representation. The convergence of the resummation results for the exponents $ν$,\ $η$ and $ω$ has been shown to improve systematically in going from low order to the highest known six-loops order. Our six-loops resummation results are very competitive to the recent six-loops Borel with conformal mapping predictions and to recent Monte Carlo simulation results. To show that precise results extend for high $N$ values, we listed the five-loops results for $ν$ which are very accurate as well. The recent seven-loops order ($g$-series) for the renormalization group functions $β,γ_{ϕ^2}$ and $γ_{m^2}$ have been resummed too. Accurate predictions for the critical coupling and the exponents $ν$, $η$ and $ω$ have been extracted from $β$,$γ_{ϕ^2}$ and $γ_{m^2}$ approximants.
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