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 Heisenberg models with local moments s = 1/2, s = 1, and s = 3/2. We conclude that the nonlinear cf model prediction for the low energy spectrum is always verified for a large enough system size. However, the crossover to the correct scaling regime is particularly slow just for the s = 1/2 Heisenberg model. The possible detection of this unexpected anomaly with finite temperature experiments on a = 1/2 isotropic quantum antiferromagnets is also discussed.