Key combinatorial problems in lattice statistical mechanics

格点统计力学中的关键组合问题。格动物的计数是组合数学中一个著名的公开问题。这些离散的结构也支撑了我们对许多物理现象的理解，包括随机介质中的聚合物坍塌和渗流，通过它们在统计力学和理论化学的许多模型中发挥的不可或缺的作用。r\n\r\n项目旨在使用精确和数值技术回答该领域的一些关键开放问题。我们预计，这将导致证明某些问题的不可解性，新的精确解的其他人，并更好地了解拓扑结构和几何形状对这些模型的行为的影响。

Key combinatorial problems in lattice statistical mechanics. The enumeration of lattice animals is a famous open problem in combinatorics. These discrete structures also underpin our understanding of many physical phenomena, including polymer collapse and percolation in random media, through the integral part they play in many models in statistical mechanics and theoretical chemistry.\r\n\r\nThe project aims to answer some key open problems in this area using exact and numerical techniques. We expect that this will lead to proofs of the insolvability of certain problems, new exact solutions of others, and a greater understanding of the effect of topology and geometry on the behaviour of these models.