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We determine the free energy of strongly interacting matter as a function ofan applied constant and uniform magnetic field. We consider N_f = 2+1 QCD withphysical quark masses, discretized on a lattice by stout improved staggeredfermions and a tree level improved Symanzik pure gauge action, and explorethree different lattice spacings. For magnetic fields of the order of thoseproduced in non-central heavy ion collisions (eB ~ 0.1 GeV^2) stronglyinteracting matter behaves like a medium with a linear response, and isparamagnetic both above and below the deconfinement transition, with asusceptibility which steeply rises in the deconfined phase. We compute theequation of state, showing that the relative increase in the pressure due tothe magnetic field gets larger around the transition, and of the order of 10 %for eB ~ 0.1 GeV^2.

Magnetic susceptibility and equation of state of N_f = 2+1 QCD with physical quark masses