Studies of Model Systems in Statistical Mechanics and Quantum Field Theory

9404747这项续期拨款涉及统计力学和量子场论的可解模型的研究。将对激发态和完备性规则的研究扩展到三态手性波茨模型的全相图。这将决定铁磁性和大规模超可积情况的激发谱如何以一种平滑的方式连接在一起，这两种情况具有明显不同的特征。本文将研究无质量不相称相的水平交叉现象如何使系统连续地从铁磁态过渡到反铁磁态。对字符的费米子和表示的研究将通过寻找扭曲仿射和超代数的表示来扩展。本理论研究处于凝聚态物理、数学物理和应用数学的交叉点。利用强大的数学技术，量子场论和统计力学之间的联系将被用来理解各种凝聚态系统在基本水平上的性质。

9404747 This renewal grant involves research on solvable models for statistical mechanics and quantum field theory. Work will be done on extending research on the excitations and the completeness rules to the full phase diagram of the three-state chiral Potts model. It will be determined how the excitation spectrum of the ferromagnetic and massively superintegrable cases, which have strikingly different features, actually join together in a smooth fashion. The manner in which the level crossing phenomena of the massless incommensurate phase allows for the systems to continuously go from the ferromagnetic case to the antiferromagnetic case will be studied. Investigations of the fermionic sum representations of characters will be extended by finding the representations for the twisted affine and super algebras. %%% This theoretical research is at the interface between condensed matter physics, mathematical physics and applied mathematics. Using powerful mathematical techniques, connections between quantum field theory and statistical mechanics will be utilized to understand the properties of various condensed matter systems at a fundamental level.