Three-dimensional simplicial gravity and degenerate triangulations

Þorleifsson, Guðmar

doi:10.1016/s0550-3213(98)00679-8

Cited by 9 publications

(13 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently the same observation has been made in three dimensions [6]. As simulations of four-dimensional simplicial gravity are notoriously time-consuming, primarily due to the large volumes needed to observe any "true" infinite-volume behavior, any reduction in the finite-size effects is of great practical importance.…”

mentioning

confidence: 68%

“…For combinatorial triangulations the (p, q)-moves are known to be ergodic for D ≤ 4 [10]. To demonstrate that the same holds true for degenerate triangulations we observe that, just as in three dimensions [6], every set of combinatorially equivalent simplexes, or sub-simplexes, can be made distinct by a finite sequence of the (p, q)-moves. Thus every degenerate triangulations can be reduced to a combinatorial one.…”

mentioning

confidence: 78%

See 1 more Smart Citation

Simulating four-dimensional simplicial gravity using degenerate triangulations

Bilke¹,

Þorleifsson

1999

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

We extend a model of four-dimensional simplicial quantum gravity to include degenerate triangulations in addition to combinatorial triangulations traditionally used. Relaxing the constraint that every 4-simplex is uniquely defined by a set of five distinct vertexes, we allow triangulations containing multiply connected simplexes and distinct simplexes defined by the same set of vertexes. We demonstrate numerically that including degenerated triangulations substantially reduces the finite-size effects in the model. In particular, we provide a strong numerical evidence for an exponential bound on the entropic growth of the ensemble of degenerate triangulations, and show that a discontinuous crumpling transition is already observed on triangulations of volume N 4 ≈ 4000. Discretized models of four-dimensional Euclidean quantum gravity, known as simplicial gravity or dynamical triangulations, have received ample attention in recent years, the hope being that in a suitable scaling limit they might provide a sensible non-perturbative definition of quantum gravity. In the simplicial gravity approach the integration over metrics is replaced by a sum over an ensemble of triangulations constructed by all possible gluings of equilateral 4-simplexes into closed (piece-wise linear) simplicial manifolds (see e.g. Ref. [1, 2]). The regularized Euclidean EinsteinHilbert action is particularly simple; it can be taken to depend on only two coupling constants, µ and κ, related to the cosmological and the inverse Newton's constants. The coupling constants are conjugate to the volume -the number of 4-simplexes -and the number of triangles in a given triangulation respectively. The regularized grand-canonical partition function thus becomes:The sum is over all distinct triangulations T ∈ T , N i is the number of i-simplexes in a triangulation T and C T denotes its symmetry factor -the number of equivalent labeling of the vertexes.

show abstract

mentioning

confidence: 68%

mentioning

confidence: 78%

Simulating four-dimensional simplicial gravity using degenerate triangulations

Bilke¹,

Þorleifsson

1999

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

show abstract

“…[17] provides evidence that this is also true for degenerate triangulations. We show the Monte Carlo time history of N 0 and the corresponding histogram for the ensemble at the peak in χ R at κ 2 = 1.672 and β = 0.…”

Section: Exploring the Phase Diagrammentioning

confidence: 80%

Exploring the Phase Diagram for Lattice Quantum Gravity

Coumbe

Laiho

2012

Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011)

View full text Add to dashboard Cite

We present evidence that a nonperturbative model of quantum gravity defined via Euclidean dynamical triangulations contains a region in parameter space with an extended 4-dimensional geometry when a non-trivial measure term is included in the gravitational path integral. Within our extended region we find a large scale spectral dimension of D s (σ → ∞) = 4.04 ± 0.26 and a Hausdorff dimension that is consistent with D H = 4 from finite size scaling. We find that the short distance spectral dimension is D s (σ → 0) ≈ 3/2, which may resolve the tension between asymptotic safety and holographic entropy scaling.

show abstract

“…The EE can also be defined with the ensemble of degenerate triangulations introduced in Ref. [6]. In this case degenerate stacked spheres (DSS) are constructed by slicing open a face and inserting -12…”

Section: Degenerate Triangulationsmentioning

confidence: 99%

The weak-coupling limit of 3D simplicial quantum gravity

Białas

Petersson

Þorleifsson

2000

Nuclear Physics B - Proceedings Supplements

View full text Add to dashboard Cite

We investigate the weak-coupling limit, κ → ∞, of 3D simplicial gravity using Monte Carlo simulations and a Strong Coupling Expansion. With a suitable modification of the measure we observe a transition from a branched polymer to a crinkled phase. However, the intrinsic geometry of the latter appears similar to that of non-generic branched polymer, probable excluding the existence of a sensible continuum limit in this phase.

show abstract

Three-dimensional simplicial gravity and degenerate triangulations

Cited by 9 publications

References 37 publications

Simulating four-dimensional simplicial gravity using degenerate triangulations

Simulating four-dimensional simplicial gravity using degenerate triangulations

Exploring the Phase Diagram for Lattice Quantum Gravity

The weak-coupling limit of 3D simplicial quantum gravity

Contact Info

Product

Resources

About