On a New Decoupling Scheme for the Retarded Green Function and Its Application to the Heisenberg Ferromagnet. II

Abstract

The decoupling problem of the Green function is investigated in a vector space. In the decoupling scheme characteristics of two kinds of Green functions defined using commutator and anticommutator are taken into account. Its lowest approximation is applied to the Heisenberg ferromagnet. If the obtained spectrum is calculated by using the symmetric decoupling, the resulting set of equations is equivalent to the one derived by Katsura and Horiguchi. If the spectrum is calculated by introducing a decoupling parameter which is determined by a condition derived from the spectral theorem, the result agrees with the one obtained by Mubayi and Lange (and by A. Oguchi), who show that the spontaneous magnetization at one and two dimensions does not exist, and that the Curie temperature at three dimensions agrees with that of the molecular field theory and the temperature dependence of spin wave energy agrees with that of Bloch’s calculations in the low temperature regions.