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首页> 外文期刊>Physical review, D >Precise critical exponents of the O(N)-symmetric quantum field model using hypergeometric-Meijer resummation
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Precise critical exponents of the O(N)-symmetric quantum field model using hypergeometric-Meijer resummation

机译：使用HyperGeometic-Meijer Resimation的O（n）-s-mymmetric量子域模型的精确临界指数

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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 ? expansion of the critical exponents of the O ( N ) -symmetric model is approximated by the hypergeometric functions F k + 1 k ? 1 . The divergent F k + 1 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-loop order. Our six-loop resummation results are very competitive to the recent six-loop 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-loop results for ν which are very accurate as well. The recent seven-loop order ( g series) for the renormalization group functions β , γ ? 2 , and γ m 2 has been resummed too. Accurate predictions for the critical coupling and the exponents ν , η , and ω have been extracted from β , γ ? 2 , and γ m 2 approximants.
机译：在这项工作中，我们表明，可以选择不同类型的超大距离近似值，以便在不同的大阶生长因子中重新调整不同类型的系列。是n！生长因子，发散系列？ o（n）-smmetric模型的临界指数的扩展由超距离函数f k + 1 k近似近似。 1。发散的f k + 1 k？然后使用其等效的MEIJER-G功能表示重新重新启动1个功能。已经显示了指数ν，η和ω的成果结果的收敛性，从而从低顺序到最高已知的六环顺序提高。我们的六环旋转突然结果与最近的六环硼尔和最近的Monte的六环硼尔和最近的蒙特仿真结果非常竞争。为了表明，精确的结果为高N值扩展，我们也列出了非常准确的ν的五环结果。最近的七循环顺序（G系列）对于重新运算组功能β，γ？图2所示，也已被重新启动γM2。对关键耦合和指数ν，η和ω的精确预测已从β，γ中提取？ 2，γm 2近似剂。

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