若干与统计物理相关的组合问题

Some Combinatorial Problems in Statistical Physics

简单介绍统计物理与纽结理论中的一些组合问题,包括反射对称图的dimer问题与支撑树的计数问题,Dimer问题的熵与边界的关系,计数平面图的完美匹配数的图压缩方法,链环多项式的计算以及Jones多项式的零点的分布问题,主要综述近年来我们在这些问题中得到的部分结果.

In this paper we first give a simple introduction to somecombinatorial problems in statistical physics and knot theory.Thenwe survey some results of our group in these respects obtained inrecent years,including enumerations of dimer and spanning trees ofgraphs with reflective symmetry,the relation bewteen dimer entropyand lattice boundary,graphical condensation method on enmueratingperfect matchings,computaions of link polynomials and zeros of theJones polynomials,etc.