Combinatorial approaches to problems in lattice statistical mechanics

解决晶格统计力学问题的组合方法

• 批准号: 341844-2007
• 负责人: Rechnitzer, Andrew
• 金额: $ 1.46万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=458610
• 关键词: Combinatorial; approaches; problems; lattice; statistical

Many of the combinatorial objects found at the interface between enumerative combinatorics and other fields, such as statistical physics, computer science and theoretical chemistry, are types of lattice animals. Lattice animals appear in models of polymers and vesicles, percolation models of phenomena such as forest fires, DNA denaturation and the Ising and Potts models of magnets. Perhaps the most famous and versatile example is the self-avoiding walk, which was introduced by Orr over 50 years ago as a model of the geometric properties of long chain polymers.

在计数组合学和其他领域（如统计物理学、计算机科学和理论化学）之间的界面上发现的许多组合对象都是格子动物。晶格动物出现在聚合物和囊泡的模型中，出现在森林火灾、DNA变性等现象的渗透模型中，出现在伊辛和波茨的磁铁模型中。 也许最著名和最通用的例子是自回避行走，它是由奥尔在50多年前作为长链聚合物几何性质的模型引入的。