Studies of Model Systems in Statistical Mechanics and Quantum Field Theory

统计力学和量子场论模型系统的研究

• 批准号: 0302758
• 负责人: Barry McCoy
• 金额: $ 30.6万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-15 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0302758&HistoricalAwards=false
• 关键词: Studies; Model; Systems; Statistical; Mechanics

This grant is funded jointly by the Divisions of Materials Research and Mathematical Sciences. The research focus is on the statistical mechanics of strongly interacting many-body systems and their connections with pure mathematics. Two topics of particular interest are the eight-vertex model and the hard-sphere fluid in D-dimensions. The results of these investigations will be used in a new textbook on statistical mechanics being written by the principal investigator (PI). The PI has discovered an unexpected new infinite dimensional symmetry of the six-vertex model at rational values of the coupling constant that explains what had previously been mysterious degeneracies in the spectrum of the transfer matrix. In the course of extending this work to the eight-vertex model the PI has discovered significant problems with the solutions of this famous thirty-year old problem. It is proposed here to solve these problems and thus provide the first complete solution for the spectrum of the model.The PI has also found that it is possible to greatly extend the computations of the virial coefficients of the hard sphere fluid. For suitable low orders numerical computations will be replaced by exact analytic computations and for higher orders significant new results will be obtained numerically. In particular the question of negative signs in the virial coefficients will be studied and the new data will be used to critically assess the existing theories of freezing.Finally, it is proposed to use new developments in the Ising model susceptibility to investigate the possibility that there are deviations from the scaling theory of critical phenomena.This research provides connections between pure mathematics and condensed matter physics. It also trains students in this interdisciplinary area of research. Finally, the proposed textbook on statistical mechanics will make this research available to a wider audience.%%%This grant is funded jointly by the Divisions of Materials Research and Mathematical Sciences. The research focus is on the statistical mechanics of strongly interacting many-body systems and their connections with pure mathematics. Two topics of particular interest are the eight-vertex model and the hard-sphere fluid in D-dimensions. The results of these investigations will be used in a new textbook on statistical mechanics being written by the principal investigator (PI). This research provides connections between pure mathematics and condensed matter physics. It also trains students in this interdisciplinary area of research. Finally, the proposed textbook on statistical mechanics will make this research available to a wider audience.***

该补助金由材料研究和数学科学部门共同资助。 研究重点是强相互作用多体系统的统计力学及其与纯数学的联系。 特别感兴趣的两个主题是八顶点模型和D维硬球流体。 这些调查的结果将被用于一个新的教科书统计力学正在编写的主要研究者（PI）。 PI发现了一个意想不到的新的无穷维对称的六顶点模型在合理的值的耦合常数，解释了什么以前是神秘的退化谱的传输矩阵。 在将这项工作扩展到八顶点模型的过程中，PI发现了这个著名的三十年老问题的解决方案的重大问题。 本文提出了解决这些问题的方法，并首次给出了该模型的谱的完整解，同时PI还发现，该方法可以大大扩展硬球流体维里系数的计算。 对于适当的低阶数值计算将取代精确的解析计算和高阶显着的新结果将获得数值。 特别是在维里系数的负号的问题将进行研究，新的数据将被用来批判性地评估现有的理论freezing.Finally，它建议使用新的发展伊辛模型的磁化率调查的可能性，有偏离标度理论的临界现象。这项研究提供了纯数学和凝聚态物理之间的连接。 它还培养学生在这个跨学科的研究领域。 最后，建议的统计力学教科书将使这项研究提供给更广泛的受众。%该补助金由材料研究和数学科学部门共同资助。 研究重点是强相互作用多体系统的统计力学及其与纯数学的联系。 特别感兴趣的两个主题是八顶点模型和D维硬球流体。 这些调查的结果将被用于一个新的教科书统计力学正在编写的主要研究者（PI）。 这项研究提供了纯数学和凝聚态物理之间的联系。 它还培养学生在这个跨学科的研究领域。 最后，拟议的统计力学教科书将使这项研究能够为更广泛的受众所用。