  We study the mean-field phase diagram of the repulsive Hubbard model in the
Lieb lattice. Far from half-filling, the most stable phases are paramagnetism
for low on-site interaction $U/t$ and ferromagnetism for high $U/t$, as in the
case of the mean-field phase diagram of the square lattice Hubbard model
obtained by Dzierzawa [\onlinecite{Dzierzawa1992}]. At half-filling, the ground
state was found to be ferrimagnetic [a $(\pi,\pi)$ spiral phase], in agreement
with a theorem by Lieb [\onlinecite{Lieb1989}]. The total magnetization
approaches Lieb's prediction as $U/t$ becomes large. As we move away from
half-filling, this ferrimagnetic phase becomes a $(q_1,q_1)$ spiral phase with
$q_1 \approx \pi$ and then undergoes a series of first-order phase transitions,
$(q_1,q_1) \rightarrow (q_1,q_2) \rightarrow (q_1,0)$, with $q_2 \approx
\pi/2$, before becoming ferromagnetic at large $U/t$ or paramagnetic at low
$U/t$.
