Studies of Model Systems in Statistical Mechanics and Quantum Field Theory

对统计力学和量子力学的研究 无限次系统的场论 自由将继续。 在过去的一年里， 统计力学是通过发现许多N 状态手征Potts模型用于研究公度 无公度相变是可解的， 拥有一个参数族的交换转移矩阵， 并且这些传递矩阵由以下曲线参数化： 一个大于一个。 这种模式，基于更高的属 曲线，已经搜索了超过15年，他们的 这一发现开辟了固体物理学的新研究领域 以及相关的代数几何领域。 过程中 该奖项的研究将是由自由能源和 这些模型的激发谱及其相关性 函数，特别是与共形场有关的函数 理论 他们还将继续寻找更多基于 在亏格大于1的曲线上， 这种模型可以在三维中找到。 调查 这些新模型之间的关系，变形的方法， 理论，可能还有弦理论。

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.