Doping dependence of the spin gap in a 2-leg ladder
  A spin-fermion model relevant for the description of cuprates ladders is studied in a path integral formalism, where, after integrating out the fermions, an effective action for the spins in term of a Fermi-determinant results. The determinant can be evaluated in the long-wavelength, low-frequency limit to all orders in the coupling constant, leading to a non-linear sigma model with doping dependent coupling constants. An explicit evaluation shows, that the spin-gap diminishes upon doping as opposed to previous mean-field treatments. 
L. Campos Venuti and A. Muramatsu