We have also extended our quantum Monte Carlo study to correlated electrons on graphene nanoribbons to investigate the edge-state magnetism. Static magnetic correlations are found to be short-ranged, but the correlation length increases rapidly with the width of the ribbon that already for moderately wide ribbons we observe a strong trend towards the mean-field type ferromagnetic correlations along the zigzag edge. These ferromagnetic correlations are furthermore shown to be accompanied by a dominant low-energy peak in the local spectral function which can be used as dynamic singature to detect the edge-state magnetism in STM experiments. Meanwhile, the magnetic excitations along the edge demonstrate the effect of an interaction-mediated antiferromagnetic coupling between the opposite edges .
 Z. Y. Meng, T. C. Lang, S. Wessel, F. F. Assaad and A. Muramatsu, "Quantum spin liquid emerging in two-dimensional correlated Dirac fermions", Nature 464, 847 (2010)