Abstract
We present the results of a high statistics Monte Carlo study of a model for four dimensional euclidean quantum gravity based on summing over triangulations. We show evidence for two phases; in one there is a logarithmic scaling of the mean linear extent with volume, whilst the other exhibits power law behaviour with exponent 1 2 . We are able to extract a finite size scaling exponent governing the growth of the susceptibility peak.
Highlights
In this article we report briefly on some new results for a model whose partition function is constructed from a sum over all random triangulations of the four dimensional sphere
Such a model has been recently studied by other groups [1, 2, 3, 4] and is a candidate for a regularised quantum theory of euclidean gravity
A crude order parameter which may be used to distinguish between different phases of the model is the average intrinsic linear extent of the system
Summary
In this article we report briefly on some new results for a model whose partition function is constructed from a sum over all random triangulations of the four dimensional sphere. The first term in the action N4 is just the number of four simplices in the triangulation T and this allows us to identify the corresponding coupling κ4 as a bare cosmological constant. The model depends on just one parameter – the node coupling κ0.
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