非极小共形场论中Schramm-Loewner演化的数值研究
Numerical study on Schramm-Loewner Evolution in nonminimal conformal field theories
摘要：
Schramm-Loewner演化（SLE）是描述二维临界统计系统分形界面的有力工具。然而，SLE的应用是建立在统计系统的量子场论描述只满足共形不变性，所谓的最小共形场论（CFTs）。我们考虑Z（N）自旋模型中的界面在N=4和N=5时的自对偶临界点。这些晶格模型描述的连续极限的非最小的CFTs的Z_N对称性的作用，除了共形的，应该考虑。我们提供的分形维数的接口，这是SLE候选人的非最小的CFTs的数值结果。我们的结果与最近的一些理论预测非常一致。
英文摘要：
The Schramm-Loewner evolution (SLE) is a powerful tool to describe fractal interfaces in 2D critical statistical systems. Yet the application of SLE is well established for statistical systems described by quantum field theories satisfying only conformal invariance, the so called minimal conformal field theories (CFTs). We consider interfaces in Z(N) spin models at their self-dual critical point for N=4 and N=5. These lattice models are described in the continuum limit by non-minimal CFTs where the role of a Z_N symmetry, in addition to the conformal one, should be taken into account. We provide numerical results on the fractal dimension of the interfaces which are SLE candidates for non-minimal CFTs. Our results are in excellent agreement with some recent theoretical predictions.
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