The Number Of Independent Sets In Lattice System

Square system and Hexagonal systems are widely applied in statistical physics and chemistry.This article mainly studyies the number of(vertex) independent sets of lattice system.There are two chapters,the first chapter studies the number of independent sets of square lattice system.In this chapter we introduce the notion of transfer matrix,and use the transfer matrix method to get the formulae of the number of independent sets in square lattice system on cylinder and torus,and list some numeric results at the same time.Using this result,we give a new way to establish the upper bounder for the double limitη=(?)f(m,n)^1/mn,where f(m,n)is the number of independent sets in the m×n grid graph G_m,n.The second chapter introduces the transfer matrix of zigzag nanotubes and armchair nanotubes,some numeric results are provided,and also deduces the formulae of independent sets of them.