临界格点模型中两种团簇边界的标度极限
The scaling limit of two cluster boundaries in critical lattice models
摘要：
利用边界共形场论（BCFT）可交替地得到Schramm-Loewner演化（SLE）中一点位于曲线一侧的概率。我们扩展了BCFT方法来处理两条曲线，例如形成集群的左边界和右边界。这证明对应于推广到SLE（kappa，rho），其中rho=2。我们推导出给定点位于两条曲线之间或两条曲线的一侧的概率。我们找到了kappa= 0，2，4，8/3，8情况下的解析解。kappa=6的结果导致在半经典近似的量子霍尔效应的平台过渡的电流分布的预测。
英文摘要：
The probability that a point is to one side of a curve in Schramm-Loewner evolution (SLE) can be obtained alternatively using boundary conformal field theory (BCFT). We extend the BCFT approach to treat two curves, forming, for example, the left and right boundaries of a cluster. This proves to correspond to a generalisation to SLE(kappa,rho), with rho=2. We derive the probabilities that a given point lies between two curves or to one side of both. We find analytic solutions for the cases kappa=0,2,4,8/3,8. The result for kappa=6 leads to predictions for the current distribution at the plateau transition in the semiclassical approximation to the quantum Hall effect.
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