  The simplest tight-binding model is used to study lattice effects on two
properties of doped graphene: i) magnetic orbital susceptibility and ii)
regular Friedel oscillations, both suppressed in the usual Dirac cone
approximation. i) An exact expression for the tight-binding magnetic
susceptibility is obtained, leading to orbital paramagnetism in graphene for a
wide range of doping levels which is relevant when compared with other
contributions. ii) Friedel oscillations in the coarse-grained charge response
are considered numerically and analytically and an explicit expression for the
response to lowest order in lattice effects is presented, showing the
restoration of regular 2d behavior, but with strong sixfold anisotropy.
