Magnetic-Field Dependence of the Static Electric Susceptibility of Glasses

We study the magnetic-field dependence of the zero-frequency electric susceptibility in glasses. Starting from the two-level tunneling systems and the nuclear spin and quadrupolar potential, we evaluate the free energy perturbatively, in terms of the quadrupolar and Zeeman energies. We find that the static susceptibility varies weakly with an external magnetic field; this effect is by six orders of magnitudes smaller than the observed dependence. One may conclude that the observed magnetic-field dependence is not a static phenomenon but of dynamic origin.