Renormalization Group Approach to Stochastic Geometric Models

水加热后变成水蒸气。这是相变现象的一个例子。当相变发生时，许多物理量会发散（或表现出奇异行为）。这是临界现象的一个例子。重归一化群法是分析临界现象最有效的工具之一。本研究的目的是将现有的重归一化群技术扩展到自旋系统的随机几何模型（如自避行走）和低温相位的分析。

Water changes into vapor when heated. This is an example of phenomena called a phase transition. When a phase transition occurs, a lot of physical quantities diverge(or show singular behavior). This is an example of critical phenomena. One of the most effective tools in the analysis of critical phenomena is the method of re normalization group. The purpose of this research is to extend the existing re normalization group techniques to the analysis of stochastic geometric models(such as self-avoiding walk) and low-temperature phase of spin systems.