二维伊辛模型的普适性与费米子观测量的共形不变性
Universality in the 2D Ising model and conformal invariance of fermionic observables
摘要：
人们普遍认为，著名的二维伊辛模型在临界状态下具有普适的、共形不变的标度极限，这一标度极限被用来推导它的许多性质。然而，没有数学证明的普适性和共形不变性曾经给出，甚至物理参数支持（先验较弱）莫比乌斯不变性。在一个大的平面图族上，我们引入了二维伊辛模型临界时的离散全纯费米子。在适当的边界条件下，我们证明了在有界域上，这些标度极限具有普适性和共形不变的标度极限，从而证明了其普适性和共形不变性。
英文摘要：
It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no mathematical proof of universality and conformal invariance has ever been given, and even physics arguments support (a priori weaker) Möbius invariance. We introduce discrete holomorphic fermions for the 2D Ising model at criticality on a large family of planar graphs. We show that on bounded domains with appropriate boundary conditions, those have universal and conformally invariant scaling limits, thus proving the universality and conformal invariance conjectures.
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