  We present a numerical study of the \lambda \phi^{4} model in three Euclidean
dimensions, where the two spatial coordinates are non-commutative (NC). We
first show the explicit phase diagram of this model on a lattice. The ordered
regime splits into a phase of uniform order and a ``striped phase''. Then we
discuss the dispersion relation, which allows us to introduce a dimensionful
lattice spacing. Thus we can study a double scaling limit to zero lattice
spacing and infinite volume, which keeps the non-commutativity parameter
constant. The dispersion relation in the disordered phase stabilizes in this
limit, which represents a non-perturbative renormalization. From its shape we
infer that the striped phase persists in the continuum, and we observe UV/IR
mixing as a non-perturbative effect.
