  In order to model pions of two-flavor QCD we consider a lattice field theory
involving two flavors of staggered quarks interacting strongly with U(1) gauge
fields. For massless quarks, this theory has an $SU_L(2)\times SU_R(2) \times
U_A(1)$ symmetry. By adding a four-fermion term we can break the U_A(1)
symmetry and thus incorporate the physics of the QCD anomaly. We can also tune
the pion decay constant F, to be small compared to the lattice cutoff by
starting with an extra fictitious dimension, thus allowing us to model low
energy pion physics in a setting similar to lattice QCD from first principles.
However, unlike lattice QCD, a major advantage of our model is that we can
easily design efficient algorithms to compute a variety of quantities in the
chiral limit. Here we show that the model reproduces the predictions of chiral
perturbation theory in the $\epsilon$-regime.
