Pinpointing Triple Point of Noncommutative Matrix Model with Curvature

Abstract: We study a Hermitian matrix model with a quartic potential, modified by a curvature term $\mathrm{tr}(R\Phi^2)$, where $R$ is a fixed external matrix. Motivated by the truncated Heisenberg algebra formulation of the Grosse-Wulkenhaar model, this term breaks unitary invariance and gives rise to an effective multitrace matrix model via perturbative expansion. We analyze the resulting action analytically and numerically, focusing on the shift of the triple point and suppression of the noncommutative stripe phase -- features linked to renormalizability. Our findings, supported by Hamiltonian Monte Carlo simulations, indicate that the curvature term drives the phase structure toward renormalizable behavior by eliminating the stripe phase.