O（N）对称$ϕ^4$模型的PDMATHAAB超几何Meijer求和临界指数
Critical Exponents of the O(N)-symmetric $ϕ^4$ Model from the \boldmath{\large{ $\varepsilon^7$}} Hypergeometric-Meijer Resummation
摘要：
我们从最近得到的$O(N)$ -对称模型的重整化群函数的七圈$g$ -展开式中提取出$\varepsilon$ -展开式。用我们最近引进的超几何Meijer重建算法对临界指数$ν,\ ω$和$η$的不同级数进行了重建。在三维空间中，对$N=0,1,2,3$和$4$的所有临界指数都得到了非常精确的结果。为了揭示在这个顺序的预测的显着改善，我们得到了$XY$模型的比热临界指数$α$的发散。从零重力液氦超流相变的比热得到了与著名的实验结果-0.0127（3）相一致的结果$-0.0123(11)$，而文献中的六圈Borel保角变换结果给出了-0.007（3）.对于具有挑战性的情况下，remation的$\varepsilon$ -扩展系列在两个维度，我们表明，我们的remation结果反映了显着改善以前的六回路remation预测。
英文摘要：
We extract the $\varepsilon$-expansion from the recently obtained seven-loop $g$-expansion for the renormalization group functions of the $O(N)$-symmetric model. The different series obtained for the critical exponents $ν,\ ω$ and $η$ have been resummed using our recently introduced hypergeometric-Meijer resummation algorithm. In three dimensions, very precise results have been obtained for all the critical exponents for $N=0,1,2,3$ and $4$. To shed light on the obvious improvement of the predictions at this order, we obtained the divergence of the specific heat critical exponent $α$ for the $XY$ model. We found the result $-0.0123(11)$ which is compatible with the famous experimental result of -0.0127(3) from the specific heat of zero gravity liquid helium superfluid transition while the six-loop Borel with conformal mapping resummation result in literature gives the value -0.007(3). For the challenging case of resummation of the $\varepsilon$-expansion series in two dimensions, we showed that our resummation results reflect a significant improvement to the previous six-loop resummation predictions.
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