Local Thermodynamical Stability of Fermion Lattice Systems

We study the magnetic moment of neutral atoms in large magnetic fields. Asymptotic formulas for the energy exist with high precision in different regions depending on how large the nuclear charge Z is compared to the magnetic field strength B. All these formulas take the splitting of the kinetic energy into Landau levels as the principal feature and then treat the electric potential as a perturbation. We prove that these approximate formulas predict correctly'(to highest order) the total magnetic moment of the atom. The proof of this fact relies on a 'virial theorem' for Coulomb systems in a constant magnetic field.