Mathematical Physics: Statistical Mechanics and Field Theory (Physics)

该项目支持凝聚态物理和高能物理中基本问题的研究。研究包括临界现象理论中的严格重整化群方法(自回避行走、渗流和库仑气体)。其他研究方向包括随机磁场中与伊辛模型有关的无序系统中的问题，以及超对称场理论模型的相结构以及相结构受指数定理约束的方式的研究。该项目涉及物理学的一般理论或数学领域，重点是随机环境中的定向聚合物、对物质理论和高能物理很重要的逆方伊辛模型、相图和量子场论模型。

This project supports research into fundamental problems in condensed matter physics and high energy physics. The research includes rigorous renormalization group methods in the theory of critical phenomena (self-avoiding walk, percolation, and Coulomb gas). Other research directions include problems in disordered systems related to the Ising model in a random magnetic field and investigations into the phase structure of supersymmetric field theory models and the way the phase structure is constrained by index theorems. This project lies in the general area of 'theoretical' or 'mathematical' of physics with emphases on directed polymers in a random environment, the inverse square Ising model, phase diagrams, and models of quantum field theory important to matter theory and high energy physics.