论文标题
$ d \ geq 3 $的小人模型的无质量阶段
Massless Phases for the Villain model in $d\geq 3$
论文作者
论文摘要
我们在$ \ mathbb {z}^d，d \ geq 3 $中以足够低的温度考虑了经典的反派旋转器模型，并证明截断的两点功能在$ | | x | x |^{2-d} $中脱节，并具有代数的融合速率。我们还为横向两点函数分别获得了相同的渐近衰变。这量化了小人模型在低温下的自发磁化结果，并严格地建立高斯旋转波的猜想在尺寸$ d \ ge 3 $中。我们认为，我们的方法扩展到有限范围的交互作用，以及其他Abelian Spin Systems和Abelian Gauge理论中的$ d \ geq 3 $。
We consider the classical Villain rotator model in $\mathbb{Z}^d, d\geq 3$ at sufficiently low temperature, and prove that the truncated two-point function decays asymptotically as $|x|^{2-d}$, with an algebraic rate of convergence. We also obtain the same asymptotic decay separately for the transversal two-point functions. This quantifies the spontaneous magnetization result for the Villain model at low temperature, and rigorously establishes the Gaussian spin-wave conjecture in dimension $d\ge 3$. We believe that our method extends to finite range interactions and to other abelian spin systems and abelian gauge theory in $d\geq 3$.
