A Green's Function Approach to the Heisenberg Model of One-, Two- and Three-Dimensional Systems

概要

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The second order Green's function is applied to discussion of the paramagnetic phase of the Heisenberg ferromagnet in the simple cubic, square and linear lattices. The decoupling parameter α is introduced to ensure the self-consistency requirement which is represented in the form <S^-_0S^+_0>=1/2 in the case of spin one-half. The high-temperature expansions yielded the results that the decoupling parameter is given by α=1-1/6zτ+(6z+5)/6^2z^2τ^2+O(τ^<-3>, the nearest neighbour correlation function by C_1=1/4zτ(1-1/2zτ+(z-5)/12z^2τ^2+O(τ^<-3> and the inverse of the susceptibility by x^<-1>=2τ-1+1/zτ+O(τ^<-2>. From the numerical solutions for α, C_1, x^<-1>, in the simple cubic lattice the infinite susceptibility turns up at the finite temperature τ_c=0.308, but the specific heat does not have a peak near τ_c. In the square and linear lattices, the susceptibility does not involve an anomaly and the specific heat has a rather broad maximum at a finite temperature. Therefore we conclude that the finite τ_c does not appear.
理論物理学刊行会の論文
1973-11-25