Renormalization Group Approach to Stochastic Geometric Models

2011 Fiscal Year Final Research Report

• Project/Area Number: 21654020
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyushu University
• Principal Investigator: HARA Takashi 九州大学, 大学院・数理学研究院, 教授 (20228620)
• Project Period (FY): 2009 – 2011
• Keywords: くりこみ群 / 臨界現象 / 自己回避ランダムウォーク / パーコレーション / イジングモデル / 低温相

Research Abstract

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.