  Non-commutative Euclidean scalar field theory is shown to have an eigenvalue
sector which is dominated by a well-defined eigenvalue density, and can be
described by a matrix model. This is established using regularizations of
R^{2n}_\theta via fuzzy spaces for the free and weakly coupled case, and
extends naturally to the non-perturbative domain. It allows to study the
renormalization of the effective potential using matrix model techniques, and
is closely related to UV/IR mixing. In particular we find a phase transition
for the \phi^4 model at strong coupling, to a phase which is identified with
the striped or matrix phase. The method is expected to be applicable in 4
dimensions, where a critical line is found which terminates at a non-trivial
point, with nonzero critical coupling. This provides evidence for a non-trivial
fixed-point for the 4-dimensional NC \phi^4 model.
