  We study the strong coupling limit of the one-flavor and two-flavor massless
't Hooft models, $large-{\cal N}_c$-color $QCD_2$, on a lattice. We use
staggered fermions and the Hamiltonian approach to lattice gauge theories. We
show that the one-flavor model is effectively described by the
antiferromagnetic Ising model, whose ground state is the vacuum of the gauge
model in the infinite coupling limit; expanding around this ground state we
derive a strong coupling expansion and compute the lowest lying hadron masses
as well as the chiral condensate of the gauge theory. Our lattice computation
well reproduces the results of the continuum theory. Baryons are massless in
the infinite coupling limit; they acquire a mass already at the second order in
the strong coupling expansion in agreement with the Witten argument that
baryons are the $QCD$ solitons.
  The spectrum and chiral condensate of the two-flavor model are effectively
described in terms of observables of the quantum antiferromagnetic Heisenberg
model. We explicitly write the lowest lying hadron masses and chiral condensate
in terms of spin-spin correlators on the ground state of the spin model. We
show that the planar limit (${\cal N}_c\longrightarrow \infty$) of the gauge
model corresponds to the large spin limit ($S\longrightarrow \infty$) of the
antiferromagnet and compute the hadron mass spectrum in this limit finding
that, also in this model, the pattern of chiral symmetry breaking of the
continuum theory is well reproduced on the lattice.
