3.10 Coupling to SU(2)-gauge fields3 Quantum Regge Calculus3.8 Two-point functions

3.9 Non-hypercubic lattices

Simulations on lattices with irregular link geometry (still with tex2html_wrap_inline2709 -topology) have been performed by Beirl et al [31, 36Jump To The Next Citation Point In The Article]. They were obtained by adding a few vertices of low coordination number to otherwise regular lattices. One finds that the average curvature tex2html_wrap_inline2489 increases from negative to positive values, even for tex2html_wrap_inline2713, as a result of the formation of spikes. In [36Jump To The Next Citation Point In The Article], the averages tex2html_wrap_inline2517 were monitored separately at the regular and the inserted vertices.

The dependence of tex2html_wrap_inline2525 on k is rather interesting: One observes two ``critical'' points, a smaller one tex2html_wrap_inline2721, where the extra vertices develop spikes, and a second one tex2html_wrap_inline2723 where the remaining vertices follow. tex2html_wrap_inline2525 undergoes a small jump at tex2html_wrap_inline2721, and a larger one at tex2html_wrap_inline2723 . There is also a transition point to a phase with collapsed simplices at large negative k, with a jump to large negative tex2html_wrap_inline2525 . Additional transition points at negative k were also found in simulations of the ``compactified'' Regge action tex2html_wrap_inline2737 (this action was discussed in [104Jump To The Next Citation Point In The Article]; see also [71Jump To The Next Citation Point In The Article, 140Jump To The Next Citation Point In The Article]) and a tex2html_wrap_inline2739 -version of Regge gravity [33]. Correlation functions at those points were computed in [34] for short distances, but no evidence for long-range correlations was found.

The same authors studied the inclusion of the higher-derivative term (15Popup Equation) in [36]. On the regular lattice, their findings for tex2html_wrap_inline2741 confirmed those by Hamber, apart from the fact that they found stable expectation values even for positive tex2html_wrap_inline2525 . Inserting irregular vertices pushes tex2html_wrap_inline2525 to larger values and leads again to the appearance of an additional transition point.



3.10 Coupling to SU(2)-gauge fields3 Quantum Regge Calculus3.8 Two-point functions

image Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll
http://www.livingreviews.org/lrr-1998-13
© Max-Planck-Gesellschaft. ISSN 1433-8351
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