Summing over all genera for d &gt; 1: a toy model

Ambjørn, J.; Durhuus, Bergfinnur; Jónsson, Thórdur

doi:10.1016/0370-2693(90)90337-6

Cited by 101 publications

(134 citation statements)

References 14 publications

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“…In addition almost all critical properties of quantum gravity can be read off directly from this function in the scaling limit. This has already been emphasized in the more general context of higher dimensional quantum gravity [10] and more specifically in two dimensions [11] (where an explicit solution was given for a toy model of branched polymers), but it is worth to repeat the arguments. First one would in general expect the exponential decay of G µ (r) to be replaced by a power fall off when m(△µ) = 0, or more precisely in the region where 1 ≪ r ≪ 1/m(△µ).…”

Section: Scaling Relationsmentioning

confidence: 88%

Scaling in quantum gravity

Ambjørn¹,

Watabiki²

1995

Nuclear Physics B

156

232

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The 2-point function is the natural object in quantum gravity for extracting critical behavior: The exponential fall off of the 2-point function with geodesic distance determines the fractal dimension d H of space-time. The integral of the 2-point function determines the entropy exponent γ, i.e. the fractal structure related to baby universes, while the short distance behavior of the 2-point function connects γ and d H by a quantum gravity version of Fisher's scaling relation. We verify this behavior in the case of 2d gravity by explicit calculation.

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Section: Scaling Relationsmentioning

confidence: 88%

Scaling in quantum gravity

Ambjørn¹,

Watabiki²

1995

Nuclear Physics B

156

232

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“…(6.1) to the value of branched polymer phase d F = 2, γ s = 1/2 [44,45,46]. It is interesting to measure the change of fractal dimension very accurately in this delicate region near c ≈ 1.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity

Kawamoto

Yotsuji

2002

Nuclear Physics B

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We numerically investigate the fractal structure of two-dimensional quantum gravity coupled to matter central charge c for −2 ≤ c ≤ 1. We reformulate Q-state Potts model into the model which can be identified as a weighted percolation cluster model and can make continuous change of Q, which relates c, on the dynamically triangulated lattice. The c-dependence of the critical coupling is measured from the percolation probability and susceptibility. The c-dependence of the string susceptibility of the quantum surface is evaluated and has very good agreement with the theoretical predictions. The c-dependence of the fractal dimension based on the finite size scaling hypothesis is measured and has excellent agreement with one of the theoretical predictions previously proposed except for the region near c ≈ 1.

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“…(4). As shown in [9,16] an object like G 1 (R; Λ) is a good probe of the fractal structure of space-time which is determined by the exponential decay of G 1 (R; Λ). We expect…”

Section: Introductionmentioning

confidence: 99%