first considered by Hotta et al [129]. It has a continuum part and a separate peak at high vertex
order. One can suppress this effect by adding a term
to the action (see also [19] for a discussion of terms of a similar nature), but this leads
to a simultaneous disappearance of the phase transition. Hotta et
al [130] have checked that for a variety of initial configurations the
singular structure is a generic feature of the model.
Catterall et al [79,
80] observed that the pair of singular vertices form the end points
of a singular link. They also offered a possible explanation for
the formation of these singular structures: Simplices of
sufficiently low dimension can maximize their local entropy by
acquiring large local volumes (see also [49] for a mean-field argument). Catterall et al [77] found
two
pseudo-critical points,
and
, associated with the creation of singular vertices and links,
which seem to merge into a single critical point
as
. One concludes that the observed phase transition in the 4d
dynamical triangulations model is driven by the appearance and
disappearance of singular geometries.
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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 |