3.7 Avoiding collapse3 Quantum Regge Calculus3.5 Influence of the measure

3.6 Evidence for a second-order transition?

The same l dl -measure was used by Hamber in an extension of a previous simulation of the higher-derivative action (16Popup Equation) [113], for lattice sizes of up to tex2html_wrap_inline2605 . At the transition point (tex2html_wrap_inline2607, tex2html_wrap_inline2609, a =0.005), the distributions of edge lengths, volumes and curvatures are smooth and Gaussian-like, and the average curvature vanishes. The location of tex2html_wrap_inline2613 from fits (17Popup Equation) to the average curvature coincide with those from [111Jump To The Next Citation Point In The Article], leading to tex2html_wrap_inline2615 . The data at a =0 do not seem to match this interpretation. This leads to the tentative conclusion that only for sufficiently large a the observed transition is of second order. It is in general ``difficult to entirely exclude the presence of a weak first-order transition, if it has a very small latent heat''. For a =0.005, one finds some evidence for a decrease in the fractal dimension as k grows.

3.7 Avoiding collapse3 Quantum Regge Calculus3.5 Influence of the measure

image Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll
http://www.livingreviews.org/lrr-1998-13
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to livrev@aei-potsdam.mpg.de