Quantum renormalization of high energy excitations in the 2D Heisenberg   antiferromagnet
  We find using Monte Carlo simulations of the spin-1/2 2D square lattice nearest neighbour quantum Heisenberg antiferromagnet that the high energy peak locations at (pi,0) and (pi/2,pi/2) differ by about 6%, (pi/2,pi/2) being the highest. This is a deviation from linear spin wave theory which predicts equal magnon energies at these points. 
Olav F. Syljuasen, Henrik M. Ronnow