Gravitational action versus entropy on simplicial lattices in four dimensions

doi:10.1016/0920-5632(93)90320-6

Nuclear Physics B - Proceedings Supplements

Volume 30, March 1993, Pages 764-767

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Abstract

We investigate quantum gravity on simplicial lattices using Regge calculus with special emphasize on the problem of the unbounded action. The role of the entropy for the path integral is discussed in detail. Our numerical results show further evidence for the existence of an entropy dominated region with well defined expectation values even for unbounded action. Analyses are performed both for the standard regular triangulation of the 4-torus and for irregularly triangulated lattices obtained by insertion of vertices using barycentric subdivision.

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Cited by (6)

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We use Monte Carlo simulations to study pure 2D Euclidean quantum gravity with R²-interaction on spherical topologies, employing Regge's formulation. We attempt to measure the string susceptibility exponent γ_str by using a finite-size scaling Ansatz in the expectation value of R², as has been done in a previous study by Bock and Vink (Nucl. Phys. B 438 (1995) 320). By considerably extending the range and statistics of their study we find that this Ansatz is plagued by large systematic errors. The R² specific string susceptibility exponent γ_str^′ is found to agree with theoretical predictions, but its determination also is subject to large systematic errors and the presence of finite-size scaling corrections. To circumvent this obstacle we suggest a new scaling Ansatz which in principle should be able to predict both, γ_str and γ_str^′. First results indicate that this requires large system sizes to reduce the uncertainties in the finite-size scaling Ansätze. Nevertheless, our investigation shows that within the achievable accuracy the numerical estimates are still compatible with analytic predictions, contrary to the recent claim by Bock and Vink.
Newtonian potential in quantum Regge gravity
1995, Nuclear Physics, Section B
We show how the Newtonian potential between two heavy masses can be computed in simplicial quantum gravity. On the lattice we compute correlations between Wilson lines associated with the heavy particles and which are closed by the lattice periodicity. We check that the continuum analog of this quantity reproduces the Newtonian potential in the weak field expansion. In the smooth anti-de Sitter-like phase, which is the only phase where a sensible lattice continuum limit can be constructed in this model, we attempt to determine the shape and mass dependence of the attractive potential close to the critical point in G. It is found that non-linear graviton interactions give rise to a potential which is Yukawa-like, with a mass parameter that decreases towards the critical point where the average curvature vanishes. In the vicinity of the critical point we give an estimate for the effective Newton constant.
Regge gravity on general triangulations
1994, Physics Letters B
We investigate quantum gravity in four dimensions using the Regge approach on triangulations of the four-torus with general, non-regular incidence matrices. We observe that the simplicial lattice with originally 31 regular vertices tends to develop spikes at irregularly inserted vertices with low coordination numbers even for vanishing gravitational coupling. Different to the regular, hypercubic lattices almost exclusively used in previous studies, we find now that the observables depend on the measure. Computations with nonvanishing gravitational coupling still reveal the existence of a region with well-defined expectation values. However, the phase structure depends on the triangulation with the regular and additional vertices undergoing two separate transitions. Even with additional higher-order terms in the action the critical behavior of the system changes with varying (local) coordination numbers.
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^☆: Supported in part by “Fonds zur Förderung der wissenschaftlichen Forschung”.

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Gravitational action versus entropy on simplicial lattices in four dimensions☆

Abstract

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