3.5 Influence of the measure3 Quantum Regge Calculus3.3 First simulations

3.4 The phase structure

Further evidence for a transition between a region of rough and smooth geometry comes from Monte Carlo simulations by Hamber [108, 111Jump To The Next Citation Point In The Article] on tex2html_wrap_inline2283 - and tex2html_wrap_inline2285 -lattices, this time with the lattice tex2html_wrap_inline2545 (see also [114] for a summary of results, and [109] for more details on the method). There is a value tex2html_wrap_inline2547 at which the average curvature vanishes. For tex2html_wrap_inline2549, the curvature becomes large and the simplices degenerate into configurations with very small volumes. He performed a simultaneous fit for tex2html_wrap_inline2547, tex2html_wrap_inline2553 and tex2html_wrap_inline2311 in the scaling relation

  equation433

This leads to a scaling exponent tex2html_wrap_inline2557, with only a weak dependence on a . There are even points with a =0 that lie in the well-defined, smooth phase. Hamber also investigated the curvature and volume susceptibilities tex2html_wrap_inline2563 and tex2html_wrap_inline2565 . At a continuous phase transition, tex2html_wrap_inline2563 should diverge, reflecting long-range correlations of a massless graviton excitation. The data obtained are not incompatible with such a scenario, but the extrapolation to the transition point tex2html_wrap_inline2547 seems somewhat ambiguous. On the other hand, one does not expect tex2html_wrap_inline2565 to diverge at tex2html_wrap_inline2547, which is corroborated by the simulations.



3.5 Influence of the measure3 Quantum Regge Calculus3.3 First simulations

image Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll
http://www.livingreviews.org/lrr-1998-13
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