  Quantum Heisenberg ferromagnets with long-range interactions decayin as
$1/r^p$ in one and two dimensions are investigated by means of the Green's
function method. It is shown that there exists a finite-temperature phase
transition in the region $d<p<2 d$ for the $d$-dimensional case and that no
transitions at any finite temperature exist for $p\ge 2 d$; the critical
temperature is also estimated. We study the magnetic properties of this model.
We calculate the critical exponents' dependence on $p$; these exponents also
satisfy a scaling relation. Some of the results were also found using the
modified spin-wave theory and are in remarkable agreement with each other.
