Fixed versus random triangulations in 2D simplicial Regge calculus

Details Fixed versus random triangulations in 2D simplicial Regge calculus Fixed versus random triangulations in 2D simplicial Regge calculus

1996-08-29

arxiv.org/abs/hep-lat/9608151v1

Phys.Lett.B390:59-63,1997

Physics

High Energy Physics

High Energy Physics - Lattice

4 latex pages + 4 ps-figs. + espcrc2.sty, poster presented by W. Janke at LATTICE96(gravity)

Scientific paper

10.1016/S0370-2693(96)01430-X

We study 2D quantum gravity on spherical topologies using the Regge calculus approach with the $dl/l$ measure. Instead of a fixed non-regular triangulation which has been used before, we study for each system size four different random triangulations, which are obtained according to the standard Voronoi-Delaunay procedure. We compare both approaches quantitatively and show that the difference in the expectation value of $R^2$ between the fixed and the random triangulation depends on the lattice size and the surface area $A$. We also try again to measure the string susceptibility exponents through a finite-size scaling Ansatz in the expectation value of an added $R^2$ interaction term in an approach where $A$ is held fixed. The string susceptibility exponent $\gamma_{str}'$ is shown to agree with theoretical predictions for the sphere, whereas the estimate for $\gamma_{str}$ appears to be too negative.

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