Dependence of Lattice Hadron Masses on External Magnetic Fields

We study the variation of the hadron masses in the presence of external magnetic fields of strength of the order of the masses themselves. We identify the main factors affecting the lattice simulation results: - the boundary discontinuities for $eB << 2\pi / L^2 a^2$. - the SU(6) choice of the hadron wave-function. We confirm qualitatively the earlier theoretical ansatz on the linear behaviour of the masses with the magnetic field and, as a by-product, we improve the lattice measurements of the nucleon magnetic moments. However our systematic and statistical errors preclude us from measuring the theoretically predicted field strength at which the proton becomes heavier than the neutron.