Surface orbital magnetism

We compute the surface correction to the density of states of a particle in a convex box subjected to a magnetic field. Applying these results to orbital magnetism, we find that at high temperatures or weak magnetic fields the surface magnetization is always paramagnetic, but oscillations appear at low temperatures. In two dimensions they can give very large paramagnetic contributions near integer values of the filling factor. Explicit formulas are given for the zero-field susceptibility and for samples with a cylindrical shape in arbitrary magnetic field.