Phase Transition in Random Noncommutative Geometries

Abstract

We present an analytic proof of the existence of phase transition in the large $N$ limit of certain random noncommutaitve geometries. These geometries can be expressed as ensembles of Dirac operators. When they reduce to single matrix ensembles, one can apply the Coulomb gas method to find the empirical spectral distribution. We elaborate on the nature of the large $N$ spectral distribution of the Dirac operator itself. Furthermore, we show that these models exhibit both a single and double cut region for certain values of the order parameter and find the exact value where the transition occurs.

arXiv commentFinal version, 15 pages, 4 figures, in the new version one reference is added. To appear in Journal of Physics A: Mathematical and Theoretical

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Cited by in corpus (11)

• Bootstrapping Dirac Ensembles
• On multimatrix models motivated by random Noncommutative Geometry I: the Functional Renormalization Group as a flow in the free algebra
• Spectral Statistics of Dirac Ensembles
• On multimatrix models motivated by random noncommutative geometry II: A Yang-Mills-Higgs matrix model
• From Noncommutative Geometry to Random Matrix Theory
• One-loop corrections to the spectral action
• BV quantization of dynamical fuzzy spectral triples
• Double scaling limits of Dirac ensembles and Liouville quantum gravity
• Computational explorations of a deformed fuzzy sphere
• Pinpointing Triple Point of Noncommutative Matrix Model with Curvature
• The loop equations for noncommutative geometries on quivers