论文标题
高几何体近似值的高阶参数化
High-Order Parametrization of the Hypergeometric-Meijer Approximants
论文作者
论文摘要
在先前的文章中，我们表明，基于大渐近行为，可以通过特定的超几个测量值的参数化近似差异。然后，通过使用Meijer G功能的等效形式对超几何近似或等效地进行分析延续进行分析延续。参数化过程涉及非线性耦合方程组的解决方案，对于使用普通PC的高阶而言，很难实现（可能是不可能）的。在这项工作中，我们扩展了近似算法，以在短时间内适应给定系列的任何顺序（高或低）。该扩展还使我们能够采用非扰动信息，例如强耦合和大渐近数据，这些信息始终用于加速收敛。我们将算法用于$ x^4 $ anharmonic振荡器的不同订单（最多O（$ 29 $））的不同订单（o（$ 29 $）），没有或没有非扰动信息。我们还考虑了$ \ Mathcal {pt} - $对称$ ix^{3} $ ANHARMONIC振荡器以及其强耦合扩展或同等Yang-Lee模型的给定$ 20 $订单的可用$ 20 $订单。对于高阶弱耦合参数化，已经获得了基态能量和描述强耦合和大级渐近行为的非扰动参数的准确结果。非扰动数据的使用非常清楚地加速了收敛。还考虑了$ SQ $晶格内易感性的高温膨胀，并导致了关键指数和临界温度的准确预测。
In previous articles, we showed that, based on large-order asymptotic behavior, one can approximate a divergent series via the parametrization of a specific hypergeometric approximant. The analytical continuation is then carried out through a Mellin-Barnes integral representation of the hypergeometric approximant or equivalently using an equivalent form of the Meijer G-Function. The parametrization process involves the solution of a non-linear set of coupled equations which is hard to achieve (might be impossible) for high orders using normal PCs. In this work, we extend the approximation algorithm to accommodate any order (high or low) of the given series in a short time. The extension also allows us to employ non-perturbative information like strong-coupling and large-order asymptotic data which are always used to accelerate the convergence. We applied the algorithm for different orders (up to O($29$)) of the ground state energy of the $x^4$ anharmonic oscillator with and without the non-perturbative information. We also considered the available $20$ orders for the ground sate energy of the $\mathcal{PT}-$symmetric $ix^{3}$ anharmonic oscillator as well as the given $20$ orders of its strong-coupling expansion or equivalently the Yang-Lee model. For high order weak-coupling parametrization, accurate results have been obtained for the ground state energy and the non-perturbative parameters describing strong-coupling and large-order asymptotic behaviors. The employment of the non-perturbative data accelerated the convergence very clearly. The High temperature expansion for the susceptibility within the $SQ$ lattice has been also considered and led to accurate prediction for the critical exponent and critical temperature.
