Scaling behaviour in random non-commutative geometries

Abstract

Random non-commutative geometries are a novel approach to taking a non-perturbative path integral over geometries. They were introduced in arxiv.org/abs/1510.01377, where a first examination was performed. During this examination we found that some geometries show indications of a phase transition. In this article we explore this phase transition further for geometries of type $(1,1)$, $(2,0)$, and $(1,3)$. We determine the pseudo critical points of these geometries and explore how some of the observables scale with the system size. We also undertake first steps towards understanding the critical behaviour through correlations and in determining critical exponents of the system.

16 pages, 16 figures (v2: updated after review)

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Cited by in corpus (10)

• Bootstrapping Dirac Ensembles
• Spectral estimators for finite non-commutative geometries
• On multimatrix models motivated by random Noncommutative Geometry I: the Functional Renormalization Group as a flow in the free algebra
• Quantum Gravity on the computer: Impressions of a workshop
• Understanding truncated non-commutative geometries through computer simulations
• 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
• Double scaling limits of Dirac ensembles and Liouville quantum gravity
• Computational explorations of a deformed fuzzy sphere