  It is well-known that non-commutative (NC) field theories at theta = infinity
are ``equivalent'' to large N matrix field theories to all orders in
perturbation theory, due to the dominance of planar diagrams. By formulating a
NC field theory on the lattice non-perturbatively and mapping it onto a twisted
reduced model, we point out that the above equivalence does not hold if the
translational symmetry of the NC field theory is broken spontaneously. As an
example we discuss NC scalar field theory, where such a spontaneous symmetry
breakdown has been confirmed by Monte Carlo simulations.
