Lattice Models and Applications

格子模型和应用

• 批准号: 9980440
• 负责人: Fa Wu
• 金额: --
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-12-15 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9980440&HistoricalAwards=false
• 关键词: Lattice; Models; Applications

9980440WuThis grant supports theoretical research on the statistical mechanics of lattice models. It is supported by the Divisions of Materials Research and Mathematical Sciences. Lattice models play an essential role in the modern theory of critical phenomena, which finds wide applications in physics, materials research and other disciplines including engineering and mathematics. This research involves theoretical studies of lattice models with emphases on exact and rigorous results and their applications.Exact analyses of lattice models have been restricted in the past mostly to systems in two dimensions. This project proposes to study 3-dimensional systems relevant to real physics. The study of a directed percolation model in three dimensions will also be conducted. In addition, investigation of 2-dimensional systems will be carried out including: the Ising model; dimer statistics; Fisher zeroes of the Potts model; quantum spin systems; applications to crystal surfaces; and, applications in mathematics.%%%This grant supports theoretical research on the statistical mechanics of lattice models. It is supported by the Divisions of Materials Research and Mathematical Sciences. Lattice models play an essential role in the modern theory of critical phenomena, which finds wide applications in physics, materials research and other disciplines including engineering and mathematics. This research involves theoretical studies of lattice models with emphases on exact and rigorous results and their applications.***

9980440Wuthis赠款支持有关晶格模型统计力学的理论研究。 它得到了材料研究和数学科学的划分的支持。 晶格模型在批判现象的现代理论中起着至关重要的作用，该理论在物理，材料研究和其他学科（包括工程和数学）中发现了广泛的应用。 这项研究涉及对晶格模型的理论研究，重点是精确和严格的结果及其应用。对晶格模型的分析过去曾经限制在两个维度上的系统。 该项目建议研究与实际物理学相关的三维系统。 还将在三个维度上对定向渗滤模型的研究。 此外，将对二维系统进行研究，包括：ISING模型；二聚体统计； Fisher的Potts模型零；量子自旋系统；应用于晶体表面；并且，数学中的应用。%%％该赠款支持有关晶格模型统计力学的理论研究。 它得到了材料研究和数学科学的划分的支持。 晶格模型在批判现象的现代理论中起着至关重要的作用，该理论在物理，材料研究和其他学科（包括工程和数学）中发现了广泛的应用。 这项研究涉及晶格模型的理论研究，重点是精确和严格的结果及其应用。***