2001/07/31 by L. Bogacz, Z. Burda, C. Petersen +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometry and complex manifolds #Noncommutative and Quantum Gravity Theories #hep-lat
paper · pdf · doi:10.1016/s0550-3213(02)00180-3
published as Nucl.Phys. B630 (2002) 339-358 · 26 pages, Latex + 23 eps figs, extended analysis of the spectrum, added figures
arxiv created 2002/03/19 · openalex publication_date 2002/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We implement fermions on dynamical random triangulation and determine numerically the spectrum of the Dirac-Wilson operator D for the system of Majorana fermions coupled to two-dimensional Euclidean quantum gravity. We study the dependence of the spectrum of the operator (epsilon D) on the hopping parameter. We find that the distributions of the lowest eigenvalues become discrete when the hopping parameter approaches the value 1/sqrt3. We show that this phenomenon is related to the behavior of the system in the 'antiferromagnetic' phase of the corresponding Ising model. Using finite size analysis we determine critical exponents controlling the scaling of the lowest eigenvalue of the spectrum including the Hausdorff dimension dH and the exponent kappa which tells us how fast the pseudo-critical value of the hopping parameter approaches its infinite volume limit.