  We discuss the lambda phi**4 model in 2- and 3-dimensional non-commutative
spaces. The mapping onto a Hermitian matrix model enables its non-perturbative
investigation by Monte Carlo simulations. The numerical results reveal a phase
where stripe patterns dominate. In d=3 we show that in this phase the
dispersion relation is deformed in the IR regime, in agreement with the
property of UV/IR mixing. This "striped phase" also occurs in d=2. For both
dimensions we provide evidence that it persists in the simultaneous limit to
the continuum and to infinite volume ("Double Scaling Limit"). This implies the
spontaneous breaking of translation symmetry.
