  We compute the magnetization of graphene in a magnetic field, taking into
account for generality the possibility of a mass gap. We concentrate on the
physical regime where quantum oscillations are not observed due to the effect
of the temperature or disorder and show that the magnetization exhibits
non-linear behaviour as a function of the applied field, reflecting the strong
non-analyticity of the two-dimensional effective action of Dirac electrons. The
necessary values of the magnetic field to observe this non-linearity vary from
a few Teslas for very clean suspended samples to 20 - 30 Teslas for good
samples on substrate. In the light of these calculations, we discuss the
effects of disorder and interactions as well as the experimental conditions
under which the predictions can be observed.

Mesoscale and Nanoscale Physics;Statistical Mechanics;Strongly Correlated Electrons;High Energy Physics - Theory