| In 1952,Lee Zhengdao and Yang zhenning reported their articles about lattice gas model and Ising model in quantum statistical mechanics.These two articles made great impact in the research of the ferromagnetic phase change, which is in what condition,the ferromagnetic could have magnetism.Two theorems in these two articles are also named Yang-Lee Theorem.And the Yang-Lee polynomial and Yang-Lee circle theorem which were referred to the Yang-Lee Theorem are also hot spots in nowadays' research.This article is mainly about discuss the research of David Ruelle,and based on this,the author tried to make a deeper research.Lemma 1:Let K1,K2 be closed subsets of C,with 0? K1,K2.IfΦ∈A2 andΦ(z1,z2)=A+Bz1+Cz2+Dz1z2≠0,whenever z1(?) K1 and z2(?) K2.Then(?)(z)=A+Dz≠0, whenever z(?)-K1K2.Lemma 2:Let Kij be closed subset of C with O(?)Kij,for i=1,2 and j=1,…,n.Ifφ1,φ2∈An,and whenever z1(?)Kil,…Zn(?)Kin,,thenφ1*φ2(z1,z2,…,zn)≠0,φi(z1,z2,…zn)≠0,whenever z1(?)-K11·K21,…,Zn(?)-K1n·K2n.Lemma 3:A step of an Asano contraction means multiplies an operator on the left side of the polynomial.Lemma 4:Perform Asano contraction to different variables of the polynomial; the operators which we get from the Asano contraction are equivalent,which means one operator is equal to the other one with an elementary transformation.Lemma 5:Pick any four variables which were divided into two groups to perform Asano contraction at the same time;it is equal to perform successive Asano contraction.Proposition:Pick any two variables ofφ(z1,z2…Zn) from z1,z2…Zn-1 to perform Asano contraction,the matrix which is referred to the operator could be written as (?),T is the matrix which refers to the operator getting from performing Asano contraction to z1,z2…zn-1 ofφ'(z1,z2…zn-1). |
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