Anomalous finite size spectrum in the S=1/2 two dimensional Heisenberg model

We study the low energy spectrum of the nearest neighbor Heisenberg model on a square lattice as a function of the total spin S. By quantum Monte Carlo simulation we compute this spectrum for the s=1/2, s=1 and s=3/2 Heisenberg models. We conclude that the nonlinear sigma model prediction for the low energy spectrum is always verified for large enough system size. However the crossover to the correct scaling regime is particularly slow just for the s=1/2 Heisenberg model. The possibility to detect this unexpected anomaly with finite temperature experiments on s=1/2 isotropic quantum antiferromagnets is also discussed.