  We construct and analyze a phase diagram of a self-interacting matrix field
coupled to 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 is crucial to renormalization. When
turned off, the triple point collapses into the origin as matrices grow larger.
When turned on, the triple point shifts away proportionally to the coupling
strength and matrix size. Coupling attenuation that renormalizes the
Grosse-Wulkenhaar model cannot contain the shifting, and the translational
symmetry-breaking stripe phase escapes to infinity, taking away the problematic
UV/IR mixing.
