Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1996-08-29
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.
Holm Christian
Janke Wolfhard
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