  We present a new approach to the problem of alternating signs for fermionic
many body Monte Carlo simulations. We demonstrate that the exchange of
identical fermions is typically short-ranged even when the underlying physics
is dominated by long distance correlations. We show that the exchange process
has a maximum characteristic range of sqrt[2*(1-f)*beta*h] lattice sites, where
beta is the inverse temperature, h is the hopping parameter, and f is the
filling fraction. We introduce the notion of permutation zones, special regions
of the lattice where identical fermions may interchange and outside of which
they may not. Using successively larger permutation zones, one can extrapolate
to obtain thermodynamic observables in regimes where direct simulation is
impossible.
