论文标题
二维高斯自由场中的水平设置渗透
Level Set Percolation in Two-Dimensional Gaussian Free Field
论文作者
论文摘要
二维高斯自由场中的水平集渗透的性质是一个难以捉摸的问题。使用循环模型映射，我们表明存在非平凡的渗透过渡，并表征了临界点。特别是，相关长度呈指数分化，关键簇是“对数分形”，其面积以线性大小为$ a \ sim l^2 / \ sqrt {\ ln ln l} $。两点连接性也随着距离的日志而衰减。我们通过数值模拟证实了我们的理论。讨论了可能的CFT解释。
The nature of level set percolation in the two-dimension Gaussian Free Field has been an elusive question. Using a loop-model mapping, we show that there is a nontrivial percolation transition, and characterize the critical point. In particular, the correlation length diverges exponentially, and the critical clusters are "logarithmic fractals", whose area scales with the linear size as $A \sim L^2 / \sqrt{\ln L}$. The two-point connectivity also decays as the log of the distance. We corroborate our theory by numerical simulations. Possible CFT interpretations are discussed.
