  Motivated by the possible mechanism for the pinning of the electronic liquid
crystal direction in YBCO as proposed in \cite{Pardini08}, we use the first
principles Monte Carlo method to study the spin 1/2 Heisenberg model with
antiferromagnetic couplings $J_{1}$ and $J_{2}$ on the square lattice. The
corresponding low-energy constants, namely the spin stiffness $\rho_s$, the
staggered magnetization density ${\cal M}_s$, the spin wave velocity $c$, as
well as the ground state energy density $e_0$ are determined by fitting the
Monte Carlo data to the predictions of magnon chiral perturbation theory. In
particular, the spin stiffnesses $\rho_{s1}$ and $\rho_{s2}$ are investigated
as a function of the ratio $J_{2}/J_{1}$ of the couplings. Although we find a
good agreement between our results with those obtained by the series expansion
method in the weakly anisotropic regime, for strong anisotropy we observe
discrepancies.
