Studies of Model Systems in Statistical Mechanics and Quantum Field Theory

对具有无限多个自由度系统的统计力学和量子场论的研究将继续进行。在过去的一年里，统计力学中有了一个重大的发现，发现许多用于研究相称不相称相变的N态手性波茨模型在具有一个参数交换转移矩阵族的意义上是可解的，并且这些转移矩阵是由大于1的格曲线参数化的。这种基于高属曲线的模型已经被研究了超过15年，它们的发现为固态物理和代数几何的相关领域开辟了新的研究领域。在这个奖项的过程中，将研究这些模型的自由能和激发谱及其相关函数，特别是它们与共形场论的联系。他们还将继续寻找更多基于属数大于1的曲线的模型，并研究是否可以在三维空间中找到这样的模型。将研究这些新模型、变形理论方法和可能的弦理论之间的关系。

The investigations into the statistical mechanics and quantum field theory of systems with an infinite number of degrees of freedom will be continued. In the past year a major discovery in statistical mechanics was made by finding that many of the N state chiral Potts models used in the study of commensurate incommensurate phase transitions are solvable in the sense of possessing a one parameter family of commuting transfer matrices, and that these transfer matrices are parametrized by curves of genus greater than one. Such models, based on higher genus curves, have been searched for over fifteen years and their discovery opens new areas of research both in solid state physics and in the related area of algebraic geometry. During the course of this award studies will be made of the free energy and excitation spectrum of these models and their correlation functions, particularly in their connection with conformal field theory. They will also continue to search for more models based on curves of genus higher than one and to investigated whether such models can be found in three dimensions. Investigations of the relation between these new models, the methods of deformation theory, and possibly string theories will be made.