  We study the orbital susceptibility of coupled energy bands with a pair of
Dirac points, as in graphene. We show that different systems having the same
zero-field energy spectrum exhibit strong differences in their orbital magnetic
response at zero energy, ranging from diamagnetism (graphene) to paramagnetism
(dice lattice). A lattice model is introduced which interpolates continuously
between these two limits. This striking behavior is related to a Berry phase
varying continuously from pi to 0. These predictions could be tested with cold
atoms in an optical lattice
