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. Inspired by the truncated Heisenberg algebra formulation of the Grosse--Wulkenhaar model, this term breaks unitary invariance and, through perturbative expansion, induces an effective multitrace matrix model. We analyze the resulting action both analytically and numerically, including Hamiltonian Monte Carlo simulations, focusing on two features closely tied to renormalizability: the shift of the triple point and the suppression of the noncommutative striped phase. Our findings show that the curvature term drives the phase structure toward renormalizable behavior by removing the striped phase in the large-$N$ limit, while also unexpectedly revealing a possible novel multi-cut phase observed at the level of finite matrix size.

References in corpus (12)

• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• The distribution of galaxy rotation in JWST Advanced Deep Extragalactic Survey
• The Continuum Phase Diagram of the 2d Non-Commutative lambda phi**4 Model
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Spontaneous breaking of translational invariance in non-commutative lambda phi^4 theory in two dimensions
• From Noncommutative Geometry to Random Matrix Theory
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Approximate treatment of noncommutative curvature in quartic matrix model
• One-loop structure of the U(1) gauge model on the truncated Heisenberg space
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Beyond second-moment approximation in fuzzy-field-theory-like matrix models
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space