  A cluster algorithm is constructed and applied to study the chiral limit of
the strongly coupled lattice Schwinger model involving staggered fermions. The
algorithm is based on a novel loop representation of the model. Finite size
scaling of the chiral susceptibility based on data from lattices of size up to
$64\times 64$ indicates the absence of long range correlations at strong
couplings. Assuming that there is no phase transition at a weaker coupling, the
results imply that all mesons acquire a mass at non-zero lattice spacings.
Although this does not violate any known physics, it is surprising since
typically one expects a single pion to remain massless at non-zero lattice
spacings in the staggered fermion formulation.
