Exact Results in Model Statistical Systems

本研究着重于模型系统统计力学的精确研究。研究集中在二维的临界渗流，重要的和广泛研究的统计系统，和farey分数自旋链的相变，一个新的和有趣的一维模型与多重分形和Monte Carol模拟的联系，模型统计力学系统的数学精确解，以及数论技术。我们的目标是获得对这些系统的新见解和理解。该项目的一个重要特点是使用纯数学技术并与数学家密切合作。本研究着重于模型系统统计力学的精确研究。研究集中在二维的临界渗流，重要的和广泛研究的统计系统，和farey分数自旋链的相变，一个新的和有趣的一维模型与多重分形和Monte Carol模拟的联系，模型统计力学系统的数学精确解，以及数论技术。我们的目标是获得对这些系统的新见解和理解。该项目的一个重要特点是使用纯数学技术并与数学家密切合作。

This research focuses on the exact study of the statistical mechanics of model systems.Research concentrates on critical percolation in two-dimensions, and important andextensively studied statistical system, and the phase transition of the farey fraction spinchain, a new and interesting one-dimensional model with connections to multifractals and Monte Carol simulations, mathematically exact solutions of model statistical mechanical systems, and techniques from number theory. The goal is to gain newinsights into, and understanding of, these systems. An important feature of the project isthe use of techniques from pure mathematics and close collaboration withmathematicians.%%%This research focuses on the exact study of the statistical mechanics of model systems.Research concentrates on critical percolation in two-dimensions, and important andextensively studied statistical system, and the phase transition of the farey fraction spinchain, a new and interesting one-dimensional model with connections to multifractals and Monte Carol simulations, mathematically exact solutions of model statistical mechanical systems, and techniques from number theory. The goal is to gain newinsights into, and understanding of, these systems. An important feature of the project isthe use of techniques from pure mathematics and close collaboration withmathematicians.