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Motivated by the possible mechanism for the pinning of the electronic liquidcrystal direction in YBCO as proposed in \cite{Pardini08}, we use the firstprinciples Monte Carlo method to study the spin 1/2 Heisenberg model withantiferromagnetic couplings $J_{1}$ and $J_{2}$ on the square lattice. Thecorresponding low-energy constants, namely the spin stiffness $\rho_s$, thestaggered magnetization density ${\cal M}_s$, the spin wave velocity $c$, aswell as the ground state energy density $e_0$ are determined by fitting theMonte Carlo data to the predictions of magnon chiral perturbation theory. Inparticular, the spin stiffnesses $\rho_{s1}$ and $\rho_{s2}$ are investigatedas a function of the ratio $J_{2}/J_{1}$ of the couplings. Although we find agood agreement between our results with those obtained by the series expansionmethod in the weakly anisotropic regime, for strong anisotropy we observediscrepancies.

Monte Carlo Determination of the Low-Energy Constants of a Spin 1/2 Heisenberg Model with Spatial Anisotropy