Spectrum of the Dirac operator coupled to two-dimensional quantum gravity

Details Spectrum of the Dirac operator coupled to two-dimensional quantum gravity Spectrum of the Dirac operator coupled to two-dimensional quantum gravity

2001-07-19

arxiv.org/abs/hep-lat/0107015v2

Nucl.Phys. B630 (2002) 339-358

Physics

High Energy Physics

High Energy Physics - Lattice

26 pages, Latex + 23 eps figs, extended analysis of the spectrum, added figures

Scientific paper

10.1016/S0550-3213(02)00180-3

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/sqrt{3}. 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 d_H and the exponent kappa which tells us how fast the pseudo-critical value of the hopping parameter approaches its infinite volume limit.

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