Universal non-linear conductivity near to an itinerant-electron ferromagnetic quantum critical point

We study the conductivity in itinerant-electron systems near to a magnetic quantum critical point. We show that, for a class of geometries, the universal power-law dependence of resistivity upon temperature may be reflected in a universal non-linear conductivity; when a strong electric field is applied, the resulting current has a universal power-law dependence upon the applied electric field. For a system with thermal equilibrium current proportional to $T^{\alpha }$ and dynamical exponent $z$, we find a non-linear resistivity proportional to $E^{\frac{z-1}{z(1+\alpha )-1}}$.