  We investigate the edge-state magnetism of graphene nanoribbons using
projective quantum Monte Carlo simulations and a self-consistent mean-field
approximation of the Hubbard model. The static magnetic correlations are found
to be short ranged. Nevertheless, the correlation length increases with the
width of the ribbon such that already for ribbons of moderate widths we observe
a strong trend towards mean-field-type ferromagnetic correlations at a zigzag
edge. These correlations are accompanied by a dominant low-energy peak in the
local spectral function and we propose that this can be used to detect
edge-state magnetism by scanning tunneling microscopy. The dynamic spin
structure factor at the edge of a ribbon exhibits an approximately linearly
dispersing collective magnonlike mode at low energies that decays into Stoner
modes beyond the energy scale where it merges into the particle-hole continuum.
