Quantum-critical behavior of itinerant ferromagnets

We study the stability of the Quantum Critical Point (QCP) for itinerant ferromagnets commonly described by the Hertz-Millis-Moriya (HMM) theory. We argue that in $D\le 3$, long-range spatial correlations associated with the Landau damping of the order parameter field generate a universal {\it negative}, non-analytic $\mathrm{\mid }q{\mathrm{\mid }}^{(D+1)\mathrm{/}2}$ contribution to the static magnetic susceptibility ${\chi }_s(q,0)$, which makes HMM theory unstable. We argue that the actual transition is either towards incommensurate ordering, or first order. We also show that singular corrections are specific to the spin problem, while charge susceptibility remains analytic at criticality.