  Domain wall fermions are defined on a lattice with an extra direction the
size of which controls the chiral properties of the theory. When gauge fields
are coupled to domain wall fermions the extra direction is treated as an
internal flavor space. Here it is found that this is not the case for scalar
fields. Instead, the interaction takes place only along the link that connects
the boundaries of the extra direction. This reveals a richness in the way
different spin particles are coupled to domain wall fermions. As an
application, 4-Fermi models are studied using large N techniques and the
results are supported by numerical simulations with N=2. It is found that the
chiral properties of domain wall fermions in these models are good across a
large range of couplings and that a phase with parity-flavor broken symmetry
can develop for negative bare masses if the number of sites along the extra
direction is finite.
