  We analyze the temperature dependence of the entropy of the spin-1/2
Heisenberg model on the three-dimensional simple-cubic lattice, for both the
case of antiferromagnetic and ferromagnetic nearest neighbor exchange
interactions. Using optimized extended ensemble quantum Monte Carlo
simulations, we extract the entropy at the critical temperature for magnetic
order from a finite-size scaling analysis. For the antiferromagnetic case, the
critical entropy density equals 0.341(5)$k_B$, whereas for the ferromagnet, a
larger value of 0.401(5) $k_B$ is obtained. We compare our simulation results
to estimates put forward recently in studies assessing means of realizing the
antiferromagnetic N\'eel state in ultra-cold fermion gases in optical lattices.

Strongly Correlated Electrons;Statistical Mechanics