Studies of Model Systems in Statistical Mechanic and QuantumField Theory

将对可解统计力学和 量子场论模型 将特别强调 放置在手性Potts模型上。 手性Potts模型 最近已经解决了它的特征值，并显示了一些 新颖的效果。 该模型表现出一种不对称的 相位，光学活动的磁模拟和Pokrovsky- 塔拉波夫跃迁。 将对此进行进一步研究 一类可能强烈影响 相互作用的费米子系统 序参量与相关性 将计算无公度相位中的函数。 的 这个可解的水平交叉系统的结果将用于 研究更一般的不可积模型。 更一般的可积 模型将被检查。 与数学的联系 单极，代数几何和拓扑场论将是 探讨了 %%% 对复杂的、相互作用的、多粒子系统的研究， 凝聚态物理和材料物理的基础。 由于这些系统的复杂性， 为了得到解决方案，经常需要进行。 然而，在这方面， 有时，物理模型，如伊辛模型，能够 准确地解决。 这些精确的解决方案提供了宝贵的 指导理解基础物理学和 精确模型和相关模型的数学结构。 的 手性Potts模型最近已被精确求解， 拟议的研究将调查该模型的应用， 物理phemonena的各种类别，并进一步探讨 解决方案的性质。

Research will be conducted on solvable statistical mechanical and quantum field theoretical models. Particular emphasis will be placed on the chiral Potts model. The chiral Potts model has recently been solved for its eigenvalues and displays a number of novel effects. The model exhibits a commensurate-incommensurate phase, the magnetic analog of optical activity and a Pokrovsky- Talapov transition. Further studies will be undertaken of this class of exact level crossing transitions which may impact strongly interacting fermion systems. Order parameters and correlation functions in the incommensurate phase will be computed. The results of this solvable level crossing system will be used to study more general non-integrable models. More general integrable models will be examined. Connections with the mathematics of monopoles, algebraic geometry and topological field theory will be explored. %%% The study of complex, interacting, many-particle systems lies at the foundation of condensed matter physics and materials physics. Because of the complexity of these systems, radical approximations frequently need to be made in order to obtain solutions. However, occasionally a physical model, such as the Ising model, is able to be solved exactly. These exact solutions provide invaluable guidance to understanding the underlying physics and the mathematical structure of the exact model and related models. The chiral Potts model has recently been solved exactly and the proposed research will investigate the application of this model to various classes of physical phemonena and further explore the nature of the solutions.