3.9 Non-hypercubic lattices3 Quantum Regge Calculus3.7 Avoiding collapse

3.8 Two-point functions

To understand the nature of the possible excitations at the phase transition, one needs to study correlation functions in the vicinity of tex2html_wrap_inline2547, which is difficult numerically. Some data are available on the connected correlation functions of the curvatures and the volumes at fixed geodesic distance d, tex2html_wrap_inline2669 and tex2html_wrap_inline2671, for lattice sizes tex2html_wrap_inline2673 [115], using a scalar field propagator to determine d . Both correlators were measured at various k -values, leading to similar results for both a =0 and a =0.005. The data, taken for tex2html_wrap_inline2683 (tex2html_wrap_inline2685 7 lattice spacings), can be fitted to decaying exponentials.

Some further data (for a =0) were reported by the Vienna group [37Jump To The Next Citation Point In The Article, 34Jump To The Next Citation Point In The Article]. These authors simply used the lattice distance n instead of the true geodesic distance d . In [37], the measure was taken to be of the form tex2html_wrap_inline2651 . They looked at tex2html_wrap_inline2695 on tex2html_wrap_inline2697 - and tex2html_wrap_inline2699 -lattices, for tex2html_wrap_inline2701 and tex2html_wrap_inline2703, and found a fast decay for all investigated values of k, and tex2html_wrap_inline2707 .



3.9 Non-hypercubic lattices3 Quantum Regge Calculus3.7 Avoiding collapse

image Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll
http://www.livingreviews.org/lrr-1998-13
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