论文标题
$ \ mathbb {z} _4 $ - 对称与XY模型的扰动功能重归于
$\mathbb{Z}_4$-symmetric perturbations to the XY model from functional renormalization
论文作者
论文摘要
我们采用非驱动重归于衍生化的衍生化扩展组的二阶来研究立方体（$ \ MATHBB {Z} _4 $ -SMMETRIC）对经典$ xy $ dimensionality $ d \ in [2,4] $中的经典$ xy $模型的扰动。在$ d = 3 $中，我们提供了对应于领先的无关扰动的特征值$ y_4 $的准确估计，并在将空间维度从$ d = 3 $降低到$ d = 2 $时遵循物理情况的演变，在这里我们大约恢复了kosterlitz-thouless-thouless物理学的发作。我们分析了与$ O（2）$ - 对称和$ \ Mathbb {Z} _4 $ - 占对称扰动有关的领先无关特征值之间的相互作用，它们的近似折叠量与$ d \至2 $。在涉及相应对称组的一个和两个不变的情况下，我们比较和讨论衍生物扩展的不同实现。
We employ the second order of the derivative expansion of the nonperturbative renormalization group to study cubic ($\mathbb{Z}_4$-symmetric) perturbations to the classical $XY$ model in dimensionality $d\in [2,4]$. In $d=3$ we provide accurate estimates of the eigenvalue $y_4$ corresponding to the leading irrelevant perturbation and follow the evolution of the physical picture upon reducing spatial dimensionality from $d=3$ towards $d=2$, where we approximately recover the onset of the Kosterlitz-Thouless physics. We analyze the interplay between the leading irrelevant eigenvalues related to $O(2)$-symmetric and $\mathbb{Z}_4$-symmetric perturbations and their approximate collapse for $d\to 2$. We compare and discuss different implementations of the derivative expansion in cases involving one and two invariants of the corresponding symmetry group.
