Simulating four-dimensional simplicial gravity using degenerate triangulations

Sven Bilke and Gudmar Thorleifsson
Phys. Rev. D 59, 124008 – Published 12 May 1999
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Abstract

We extend a model of four-dimensional simplicial quantum gravity to include degenerate triangulations in addition to the combinatorial triangulations traditionally used. Relaxing the constraint that every 4-simplex is uniquely defined by a set of five distinct vertices, we allow triangulations containing multiply connected simplexes and distinct simplexes defined by the same set of vertices. We demonstrate numerically that including degenerated triangulations substantially reduces the finite-size effects in the model. In particular, we provide strong numerical evidence for an exponential bound on the entropic growth of the ensemble of degenerate triangulations, and show that a discontinuous crumpling transition is already observed on triangulations of volume N44000.

  • Received 26 October 1998

DOI:https://doi.org/10.1103/PhysRevD.59.124008

©1999 American Physical Society

Authors & Affiliations

Sven Bilke

  • Institute of Theoretical Physics, University of Amsterdam, 1018 XE Amsterdam, The Netherlands

Gudmar Thorleifsson

  • Facultät für Physik, Universität Bielefeld D-33615, Bielefeld, Germany

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Vol. 59, Iss. 12 — 15 June 1999

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