论文标题
O（n）-symmetric $ ϕ^4 $模型的关键指数来自\ boldmath {\ ligal {$ \ varepsilon^7 $}} hypermetric-meijer重新召集
Critical Exponents of the O(N)-symmetric $ϕ^4$ Model from the \boldmath{\large{ $\varepsilon^7$}} Hypergeometric-Meijer Resummation
论文作者
论文摘要
我们从最近获得的$ o（n）$ - 对称模型的重归其化组功能中提取$ \ varepsilon $ - expansion。使用我们最近引入的超几何 - meijer重新召集算法重新定义了针对关键指数$ν，\ω$和$η$获得的不同系列。在三个维度中，为$ n = 0,1,2,3 $和$ 4 $的所有关键指数获得了非常精确的结果。为了阐明该订单下预测的明显改善，我们获得了$ XY $模型的特定热量指数$α$的分歧。我们发现了结果$ -0.0123（11）$，它与零重力液体液氦超级流体过渡的特定热量兼容-0.0127（3），而六循环的borel具有综合映射的重新介绍，导致文献中值为-0.007（3）。对于在二维中重新汇总$ \ varepsilon $ expansion系列的具有挑战性的案例，我们表明我们的重新召集结果反映了对先前的六环重新召集预测的显着改善。
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.
