Motivated by some previous work on fermions on random lattices and by
suggestions that impurities could trigger parity breaking in 2d crystals, we
have analyzed the spectrum of the Dirac equation on a two dimensional square
lattice where sites have been removed randomly --- a doped lattice. We have
found that the system is well described by a sine-Gordon action. The solitons
of this model are the lattice fermions, which pick a quartic interaction due to
the doping and become Thirring fermions. They also get an effective mass
different from the lagrangian mass. The system seems to exhibit spontaneous
symmetry breaking, exactly as it happens for a randomly triangulated lattice.
The associated ``Goldstone boson" is the sine-Gordon scalar. We argue, however,
that the peculiar behaviour of the chiral condensate is due to finite size
effects.Comment: 11 page