The dependence of
on
k
is rather interesting: One observes
two
``critical'' points, a smaller one
, where the extra vertices develop spikes, and a second one
where the remaining vertices follow.
undergoes a small jump at
, and a larger one at
. There is also a transition point to a phase with collapsed
simplices at large negative
k, with a jump to large negative
. Additional transition points at negative
k
were also found in simulations of the ``compactified'' Regge
action
(this action was discussed in [104
]; see also [71
,
140
]) and a
-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 (15) in [36]. On the regular lattice, their findings for
confirmed those by Hamber, apart from the fact that they found
stable expectation values even for positive
. Inserting irregular vertices pushes
to larger values and leads again to the appearance of an
additional transition point.
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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 |