Abstract
The second order Green's function is appli~d 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 C1=1/24r-1+0(r-2), (b) the inverse susceptibility x-1=2-r-1 +O(r- 1), (c) the specific heat goes as r-2. These temperature dependences of the thermody namic quantities at high temperatures agree with the exact high temperature expansion theo ry up to the order of r 0 for x- 1• Numerical solutions yield the nearest neighbour correlation function at the Curie temperature C 1 (r.) =0.109 where the Curie temperature r.=0.245, which is compared with the Pade value r.=0.279. Near rc, x- 1 behaves as (r-r.)T, with r=l.95 ±0.01. '
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