  We perform numerical simulations of the 2-d antiferromagnetic quantum
Heisenberg model using an efficient cluster algorithm. Comparing the finite
size and finite temperature effects of various quantities with recent results
from chiral perturbation theory we are able to determine the low energy
parameters of the system very precisely. We find $e_0 = - 0.6693(1) J/a^2$ for
the ground state energy density, ${\cal M}_s = 0.3074(4)/a^2$ for the staggered
magnetization, $\hbar c = 1.68(1) J a$ for the spin wave velocity and $\rho_s =
0.186(4) J$ for the spin stiffness. Our results agree with experimental data
for the undoped precursor insulators of high-$T_c$ superconductors.
