Renormalization Group Approach to Stochastic Geometric Models

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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.