Saberi A A, Niry M D, Fazeli S M, Rahimi Tabar M R, Rouhani S
Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 May;77(5 Pt 1):051607. doi: 10.1103/PhysRevE.77.051607. Epub 2008 May 23.
The statistics of isoheight lines in the (2+1) -dimensional Kardar-Parisi-Zhang (KPZ) model is shown to be conformally invariant and equivalent to those of self-avoiding random walks. This leads to a rich variety of exact analytical results for the KPZ dynamics. We present direct evidence that the isoheight lines can be described by the family of conformally invariant curves called Schramm-Loewner evolution (or SLE_{kappa} ) with diffusivity kappa=8/3 . It is shown that the absence of the nonlinear term in the KPZ equation will change the diffusivity kappa from 8/3 to 4, indicating that the isoheight lines of the Edwards-Wilkinson surface are also conformally invariant and belong to the universality class of domain walls in the O(2) spin model.
（2 + 1）维 Kardar-Parisi-Zhang（KPZ）模型中等高线的统计被证明是共形不变的，并且等同于自回避随机游走的统计。这为 KPZ 动力学带来了丰富多样的精确解析结果。我们给出直接证据表明，高线可以由称为施拉姆 - 洛厄纳演化（或 SLE_κ）的共形不变曲线族来描述，其中扩散率 κ = 8/3。结果表明，KPZ 方程中非线性项的缺失会使扩散率 κ 从 8/3 变为 4，这表明爱德华兹 - 威尔金森表面的高线也是共形不变的，并且属于 O(2) 自旋模型中畴壁的普适类。
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