Numerical study on electron-electron interaction and ferromagnetic fluctuation in graphene

Within the Hubbard model on a honeycomb lattice, we investigate the effect of electron-electron interactions and ferromagnetic fluctuations in graphene numerically. We find that the system in the filling region $<$$n$$>$=1.60-1.90 shows a short-ranged ferromagnetic correlation, and the on-site Coulomb interaction tends to strengthen ferromagnetic fluctuation slightly. Furthermore, the ferromagnetic fluctuation is strengthened markedly as the next-nearest neighbor hoping energy increases, which indicate that the next-nearest neighbor hoping term plays an important role in graphene since it breaks the particle-hole symmetry.