We determine universal critical exponents that describe the continuous phase transitions in different dimensions of space. We use continued functions without any external unknown parameters to obtain analytic continuation for the recently derived 7-loop weak coupling \(\epsilon \)-expansions from O(n)-symmetric \(\phi ^4\) field theory. Employing a new blended continued function, we obtain critical exponent \(\alpha =-0.0121(22)\) for the phase transition of superfluid helium which matches closely with the most accurate experimental value. This result addresses the long-standing discrepancy between the theoretical predictions and precise experimental result of O(2) \(\phi ^4\) model known as ”\(\lambda \)-point specific heat experimental anomaly”. Further we have also examined the applicability of such continued functions in other examples of field theories.

我们确定通用的临界指数，这些指数描述了空间不同维度上的连续相变。我们使用没有任何外部未知参数的连续函数来从O（n）对称\（\ phi ^ 4 \）场理论中获得最近导出的7环弱耦合\（\ epsilon \）-展开的解析连续性。通过使用新的混合连续函数，我们获得了与最精确的实验值紧密匹配的超流体氦的相变临界指数\（\ alpha = -0.0121（22）\）。该结果解决了O（2）的理论预测与精确实验结果之间的长期差异。\（\ phi ^ 4 \）模型称为“ \（\ lambda \）-点比热实验异常”。此外，我们还在现场理论的其他示例中研究了此类连续功能的适用性。