Zeeman spin-splitting-frequency renormalization in disordered interacting electronic systems

At sufficiently low temperature, the magnetic field affects the thermodynamic and transport properties of interacting disordered electronic systems via the Zeeman spin-splitting frequency. In this paper, we show that this frequency always appears multiplied by the spin Fermi-liquid factor and altogether renormalizes as the spin susceptibility, resulting in an effectively enhanced magnetic field. This result is derived from perturbation theory and renormalization-group analysis, and it is shown to implement the Ward identities we derive for the spin vertices in the presence of the magnetic field. We also discuss the implications of our result in the weak- and strong-localization regime for various physical quantities like the density of states, the conductivity, the specific heat, and for the crossover behavior around the nonmagnetic fixed point.