  Non-commutative (NC) field theories can be mapped onto twisted matrix models.
This mapping enables their Monte Carlo simulation, where the large N limit of
the matrix models describes the continuum limit of NC field theory. First we
present numeric results for 2d NC gauge theory of rank 1, which turns out to be
renormalizable. The area law for the Wilson loop holds at small area, but at
large area we observe a rotating phase, which corresponds to an Aharonov-Bohm
effect. Next we investigate the NC phi^4 model in d=3 and explore its phase
diagram. Our results agree with a conjecture by Gubser and Sondhi in d=4, who
predicted that the ordered regime splits into a uniform phase and a phase
dominated by stripe patterns.
