Monte Carlo simulations of random non-commutative geometries

Barrett, John W. and Glaser, Lisa (2016) Monte Carlo simulations of random non-commutative geometries. Journal of Physics A: Mathematical and Theoretical, 49 (24). ISSN 1751-8113

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Abstract

Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated using Monte Carlo simulations to compute the integrals. Various qualitatively different types of behaviour of these random Dirac operators are exhibited. Some features are explained in terms of the theory of random matrices but other phenomena remain mysterious. Some of the models with a quartic action of symmetry-breaking type display a phase transition. Close to the phase transition the spectrum of a typical Dirac operator shows manifold-like behaviour for the eigenvalues below a cut-off scale.

Item Type: Article
Additional Information: This is an author-created, un-copyedited version of an article accepted for publication in the Journal of Physics A: Mathematical and Theoretical. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1751-8113/49/24/245001.
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1088/1751-8113/49/24/245001
Depositing User: Eprints, Support
Date Deposited: 20 May 2016 19:14
Last Modified: 17 Sep 2016 23:02
URI: http://eprints.nottingham.ac.uk/id/eprint/33251

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