论文标题
使用超几何 - meijer重新调整O（N） - 对称量子场模型的精确临界指数
Precise Critical Exponents of the O(N)-Symmetric Quantum field Model using Hypergeometric-Meijer Resummation
论文作者
论文摘要
在这项工作中，我们表明可以选择不同类型的高几何近似值，以重新召集具有不同大阶生长因子的发散序列。作为$ n！$增长因子，$ \ varepsilon $ - $ O（n）$ - 对称模型的$ \ varepsilon $扩展的分歧系列近几幅函数近似于$ _ {k+1} f_ {k-1} $。然后，使用其等效的Meijer-G函数表示，将发散$ _ {K+1} f_ {K-1} $函数重新定义。已证明，指数$ν$，\ $η$和$ω$的重新召集结果的收敛性可系统地改进，从低阶到最高的六环订单。我们的六环重新召集结果与最近的六环预测和最近的蒙特卡洛模拟结果非常有竞争力。为了表明，对于高$ n $值的精确结果扩展了，我们列出了$ν$的五环结果，这些结果也非常准确。重新归一化组功能$β，γ_{ϕ^2} $和$γ_{m^2} $的近期七环订单（$ g $ series）也得到了重新定位。从$β$，$γ_{ϕ^2} $和$γ_{m^2} $近似值中提取了关键耦合和指数$ν$，$η$和$ω$的准确预测。
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.
