A Green's Function Theory of the Heisenberg Paramagnet

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 lattice. In the case of spin one-half the products of the spin operators at the same lattice point are treated exactly. Analytical evaluations are performed at high temperatures to yield the results that (a) the nearest neighbour correlation function C_1=1/24τ^<-1>+O(τ<-2>), (b) the inverse susceptibility X^<-1>=2τ-1+O(τ<-1>), (c) the specific heat goes as (τ<-2>). These temperature dependences of the thermodynamic quantities at high temperatures agree with the exact high temperature expansion theory up to the order of τ^0 for x^<-1>. Numerical solutions yield the nearest neighbour correlation function at the Curie temperature C_1(τ_c)=0.109 where the Curie temperature (τ_c)=0.245, which is compared with the Pade value (τ_c)=0.279. Near (τ_c), x^<-1> behaves as (τ-τ_c)^γ, with γ=1.95 ±0.01.
理論物理学刊行会の論文
1973-07-25