  We construct and analyze the phase diagram of a self-interacting matrix field
in two dimensions coupled to the curvature of the non-commutative truncated
Heisenberg space. In the infinite size limit, the model reduces to the
renormalizable Grosse-Wulkenhaar's. The curvature term proves crucial for the
diagram's structure: when turned off, the triple point collapses into the
origin as matrices grow larger; when turned on, the triple point recedes from
the origin proportionally to the coupling strength and the matrix size. The
coupling attenuation that turns the Grosse-Wulkenhaar model into a
renormalizable version of the $\phi^4_\star$-model cannot stop the triple point
recession. As a result, the stripe phase escapes to infinity, removing the
problems with UV/IR mixing.
