Lattice Models and Applications

9980440Wu这笔赠款支持对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部的支持。晶格模型在现代临界现象理论中起着至关重要的作用，在物理学、材料研究以及包括工程和数学在内的其他学科中都有广泛的应用。这项研究涉及到格子模型的理论研究，侧重于精确和严谨的结果及其应用。过去对格子模型的精确分析大多局限于二维系统。这个项目计划研究与真实物理相关的三维系统。还将对三维定向渗流模型进行研究。此外，还将开展对二维系统的研究，包括：伊辛模型；二聚体统计；Potts模型的Fisher零点；量子自旋系统；在晶体表面的应用；以及在数学上的应用。%这笔赠款支持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部的支持。晶格模型在现代临界现象理论中起着至关重要的作用，在物理学、材料研究以及包括工程和数学在内的其他学科中都有广泛的应用。这项研究涉及到格子模型的理论研究，重点是精确和严谨的结果及其应用。

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.***