论文标题
$φ^4 $ - 向量型号的稳定性：四环$ \ varepsilon $扩展研究
Stability of $φ^4$-vector model: four-loop $\varepsilon$ expansion study
论文作者
论文摘要
分析了$ O（n）$ - 对称固定点在$φ^4 $ field理论中存在矢量式术语（$ \ sim hp_αp_β$）的稳定性。为此，获得了最小减法（MS）方案中的$ d = 4-2 \ varepsilon $中的四环重归其化组扩展。该动作中经常被忽视的术语需要对新固定点的现有问题及其稳定性问题进行详细而准确的研究，这可能会导致相应的普遍性类别的变化。我们发现，在扰动理论的较低顺序中，只有$ o（n）$ - 对称固定点$（g _ {\ text {h}}}，h = 0）$，但稳定性指数的相应正值$ω_h$很小。这导致我们通过计算$ω_h$的$ \ varepsilon $扩展的4循环贡献来分析较高的扰动理论中的常数，这应该足以推断该指数的积极性或负效率。事实证明，该值无疑是正面的，尽管即使在较高的循环中仍然很小：0.0156（3）$。这些结果导致在分析$ O（n）$对称模型的临界行为时，应在动作中忽略相应的矢量项。同时，$ω_h$的小价值表明，对临界缩放的相应校正在较大范围内很重要。
The stability of $O(n)$-symmetric fixed point regarding the presence of vector-field term ($\sim h p_αp_β$) in the $φ^4$ field theory is analyzed. For this purpose, the four-loop renormalization group expansions in $d=4-2\varepsilon$ within Minimal Subtraction (MS) scheme are obtained. This frequently neglected term in the action requires a detailed and accurate study on the issue of existing of new fixed points and their stability, that can lead to the possible change of the corresponding universality class. We found that within lower order of perturbation theory the only $O(n)$-symmetric fixed point $(g_{\text{H}},h=0)$ exists but the corresponding positive value of stability exponent $ω_h$ is tiny. This led us to analyze this constant in higher orders of perturbation theory by calculating the 4-loop contributions to the $\varepsilon$ expansion for $ω_h$, that should be enough to infer positivity or negativity of this exponent. The value turned out to be undoubtedly positive, although still small even in higher loops: $0.0156(3)$. These results cause that the corresponding vector term should be neglected in the action when analyzing the critical behaviour of $O(n)$-symmetric model. At the same time, the small value of the $ω_h$ shows that the corresponding corrections to the critical scaling are significant in a wide range.
