  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.
