  We study a Hermitian matrix model with the standard quartic potential amended
by a $\mathrm{tr}(R\Phi^2)$ term for fixed external matrix $R$. This is
motivated by a curvature term in the truncated Heisenberg algebra formulation
of the Grosse-Wulkenhaar model -- a renormalizable noncommutative field theory.
The extra term breaks the unitary symmetry of the action and leads, after
perturbative calculation of the unitary integral, to an effective multitrace
matrix model. Accompanying the analytical treatment of this multitrace
approximation, we also study the model numerically by Monte Carlo simulations.
The phase structure of the model is investigated, and a modified phase diagram
is identified. We observe a shift of the transition line between the 1-cut and
2-cut phases of the theory that is consistent with the previous numerical
simulations and also with the removal of the noncommutative phase in the
Grosse-Wulkenhaar model.
