Magnetic properties of the t-J model at low doping

The analysis of Landau damping shows that in this case, even in the presence of doping, the dynamical critical exponent z=1, as a consequence of coupling of the dopant holes to a spin current, as opposed to a spin density. This result agrees with experimental observations in the underdoped region of high temperature superconductors, and departs from the one obtained by Hertz and Millis (z=2) in the case of spin density waves in the Hubbard model.