  We perform molecular dynamics and Monte Carlo simulations of two-dimensional
melting with dipole-dipole interactions. Both static and dynamic behaviors are
examined. In the isotropic liquid phase, the bond orientational correlation
length 6 and susceptibility 6 are measured, and the data are fitted to the
theoretical ansatz. An algebraic decay is detected for both spatial and
temporal bond orientational correlation functions in an intermediate
temperature regime, and it provides an explicit evidence for the existence of
the hexatic phase. From the finite-size scaling analysis of the global bond
orientational order parameter, the disclination unbinding temperature Ti is
estimated. In addition, from dynamic Monte Carlo simulations of the positional
order parameter, we extract the critical exponents at the dislocation unbinding
temperature Tm. All the results are in agreement with those from experiments
and support the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory.
