  We investigate two models in non-commutative (NC) field theory by means of
Monte Carlo simulations. Even if we start from the Euclidean lattice
formulation, such simulations are only feasible after mapping the systems onto
dimensionally reduced matrix models. Using this technique, we measure Wilson
loops in 2d NC gauge theory of rank 1. It turns out that they are
non-perturbatively renormalizable, and the phase follows an Aharonov-Bohm
effect if we identify \theta = 1/B. Next we study the 3d \lambda \phi^{4} model
with two NC coordinates, where we present new results for the correlators and
the dispersion relation. We further reveal the explicit phase diagram. The
ordered regime splits into a uniform and a striped phase, as it was
qualitatively conjectured before. We also confirm the recent observation by
Ambjorn and Catterall that such stripes occur even in d=2, although they imply
the spontaneous breaking of translation symmetry. However, in d=3 and d=2 we
observe only patterns of two stripes to be stable in the range of parameters
investigated.
