  We discuss recent results obtained for the Hamiltonian Mean Field model. The
model describes a system of N fully-coupled particles in one dimension and
shows a second-order phase transition from a clustered phase to a homogeneous
one when the energy is increased. Strong chaos is found in correspondence to
the critical point on top of a weak chaotic regime which characterizes the
motion at low energies. For a small region around the critical point, we find
anomalous (enhanced) diffusion and L\'evy walks in a transient temporal regime
before the system relaxes to equilibrium.
