  We consider the ferromagnetic quantum Heisenberg model in one dimension, for
any spin $S\geq 1/2$. We give upper and lower bounds on the free energy,
proving that at low temperature it is asymptotically equal to the one of an
ideal Bose gas of magnons, as predicted by the spin-wave approximation. The
trial state used in the upper bound yields an analogous estimate also in the
case of two spatial dimensions, which is believed to be sharp at low
temperature.
