SLE $(κ,ρ)$对临界统计模型的观察
Observation of SLE$(κ,ρ)$ on the Critical Statistical Models
摘要：
Schramm-Loewner Evolution（SLE）是一个随机过程，它使用一个实参数$κ$帮助对关键统计模型进行分类。SLE的数值研究通常涉及在实轴上开始和结束的曲线。为了减少研究临界曲线的数值误差，从实轴开始，并在其上结束，我们已经使用流体动力学归一化SLE（$κ,ρ$），这是一个随机微分方程，假设来管理这样的曲线。在本文中，我们直接验证了这一假设，并数值应用于阿贝尔沙堆模型（ASM）（$κ=2$）和临界逾渗（$κ=6$）的域壁曲线。我们观察到，这种方法是更可靠的分析界面回路。
英文摘要：
Schramm-Loewner Evolution (SLE) is a stochastic process that helps classify critical statistical models using one real parameter $κ$. Numerical study of SLE often involves curves that start and end on the real axis. To reduce numerical errors in studying the critical curves which start from the real axis and end on it, we have used hydrodynamically normalized SLE($κ,ρ$) which is a stochastic differential equation that is hypothesized to govern such curves. In this paper we directly verify this hypothesis and numerically apply this formalism to the domain wall curves of the Abelian Sandpile Model (ASM) ($κ=2$) and critical percolation ($κ=6$). We observe that this method is more reliable for analyzing interface loops.
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