Ferromagnetic Instability in Disordered Systems: A Hartree-Fock Approach

It was realized two decades ago that two dimensional diffusive Fermi liquid is unstable against arbitrarily weak electronic interactions. Recently, using the nonlinear sigma model developed by Finkelstein, several authors showed the instability gives rise to a ferromagnetic state. In this work, we consider electrons moving in a random potential with the following interaction: $-J\vec{S(x)}\cdot\vec{S(x')}$. We calculate the electron self energy and find that in two dimensions, the total energy is always minimized by ferromagnetic phase, while in three dimensions, ferromagnetism occurs only if $J$ exceeds a critical value proportional to the conductivity. Although the model and the calculation method are apparently different from the ones used before, the results are in qualitative agreement, which shows the robustness of the ferromagnetic instability in interacting disordered systems.