Universality in the 2D Ising model and conformal invariance of fermionic observables
Universality in the 2D Ising model and conformal invariance of fermionic observables
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DOI：
10.1007/s00222-011-0371-2
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发表时间：
2012-09-01
影响因子：
3.1
通讯作者：
Smirnov, Stanislav
中科院分区：
文献类型：
--
作者：
Chelkak, Dmitry;Smirnov, Stanislav
人们普遍认为，著名的临界点二维伊辛模型具有通用且共形不变的标度极限，该极限用于推导其许多属性。然而，没有给出任何数学证明，甚至物理学论证也支持（先验较弱的）莫比乌斯不变性。我们为二维伊辛模型在一大类平面图上的临界点引入了离散全纯费米子。我们证明，在具有适当边界条件的有界域上，它们具有通用和共形不变的标度限制，从而证明了普遍性和共形不变猜想。
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 has ever been given, and even physics arguments support (a priori weaker) Mobius 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.