  Two approaches are pursued to determine the magnetization of the QCD vacuum
at zero and nonzero temperatures using lattice simulations. The first method
builds on pressure anisotropies which are induced by the magnetic field on the
lattice. The second approach is a novel, generalized version of the integral
method, which exploits the independence of the theory on B for asymptotically
large quark masses. Both approaches give consistent results and confirm that
the QCD medium is paramagnetic. Finally, an interesting relation between QCD
paramagnetism, magnetic catalysis of the QCD condensate and the QED
beta-function is pointed out.
