An attempt was made by Ambjørn and Jurkiewicz [13] to link the non-recognizability to the presence of large-
barriers, which should manifest themselves as an obstacle to
cooling down an large initial random triangulation to the minimal
-configuration. No such barriers were found for system sizes
, but unfortunately they were also absent for an analogous
simulation (for
) performed by de Bakker [86] for
, which is not recognizable.
Since the local moves alter the volume, one works in practice
with a ``quasi-canonical'' ensemble, i.e. one uses the grand
canonical ensemble
, but adds a potential term to the action so that the only
relevant contributions come from states in an interval
around the target volume
V
. There have been several cross-checks which have found no
dependence of the results on the width and shape of the potential
term [79
,
51
], but the lattice sizes and fluctuations may still be too small
to detect a potential failure of ergodicity, c.f. [53
].
To improve the efficiency of the algorithm, Ambjørn and
Jurkiewicz [14] used additional global (topology-preserving) ``baby universe
surgery'' moves, by cutting and gluing pieces of the simplicial
complex . In the branched polymer phase, one can estimate the
entropy exponent
, assuming a behaviour of the form
, by counting baby universes of various sizes. At the transition
point, one finds
[10,
14
,
97]. More recently, Egawa et al [98] have reported a value of
.
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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 |