Low-Temperature Magnetization of theS=12Heisenberg Ferromagnet

The low-temperature magnetization of the $S=\frac{1}{2}$ Heisenberg ferromagnet has been investigated by the method of double-time temperature-dependent Green functions. The equation for the lowest order Green function and the equation for the next higher order Green function, truncated to order $〈n〉=\frac{1}{2}-〈S^z〉$, were solved. The low-temperature magnetization so obtained was found to agree with that obtained by Dyson. In particular, an argument is presented which suggests that the $T^3$ term, which has previously plagued this method, does indeed vanish.