The spectral dimension of the branched polymers phase of two-dimensional quantum gravity

John F. Wheater; Thordur Jonsson

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The spectral dimension of the branched polymers phase of two-dimensional quantum gravity

Thordur Jonsson, John F. Wheater

High Energy Physics - Lattice · Submitted 4 Oct 1997

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show analytically that the spectral dimension of such a branched polymer phase is four thirds.

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arXiv IDhep-lat/9710024 (version 1)

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CitationJohn F. Wheater, Thordur Jonsson. "The spectral dimension of the branched polymers phase of two-dimensional quantum gravity." arXiv:hep-lat/9710024 (1997). https://pith.science/paper/F6JYRVBK

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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The metric of two-dimensional quantum gravity interacting with conformal matter is believed to collapse to a branched polymer metric when the central charge c>1. We show analytically that the spectral dimension of such a branched polymer phase is four thirds. This is in good agreement with numerical simulations for large c.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The metric of two-dimensional quantum gravity interacting with conformal matter is believed to collapse to a branched polymer metric when the central charge c>1.	background 1.00	0.04	0.04	hedged possibility 0.85
s1	We show analytically that the spectral dimension of such a branched polymer phase is four thirds.	result 0.99	0.96	0.93	asserted 1.00
s2	This is in good agreement with numerical simulations for large c.	interpretation 0.70	0.28	0.07	asserted 0.66

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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full text
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T body sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

The metric of two-dimensional quantum gravity interacting with conformal matter is believed to collapse to a branched polymer metric when the central charge c>1. We show analytically that the spectral dimension of such a branched polymer phase is four thirds. This is in good agreement with numerical simulations for large c.

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Spectral Dimension of the Universe
hep-th 2005-05 conditional novelty 8.0 of 10

Diffusion on simulated causal dynamical triangulation universes yields a spectral dimension that falls from four at large distances to roughly two at short distances.
Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
hep-th 2009-02 conditional novelty 7.0 of 10

A diffusion-based spectral dimension of spacetimes with anisotropic scaling is d_s = 1 + D/z, which for 3+1 dimensional Lifshitz gravity runs from four at large scales to two at short scales.
Cosmology of the Lifshitz universe
hep-th 2009-04 conditional novelty 6.0 of 10

A Lifshitz scalar coupled to Horava gravity produces bouncing vacuum cosmologies but, under detailed balance, an inflationary spectrum that is exponentially scale-dependent and observationally unviable.
Melons are branched polymers
math-ph 2013-02 conditional novelty 5.0 of 10

Melonic graphs, the leading-order graphs of tensor models, have Hausdorff dimension 2 and spectral dimension 4/3, matching branched polymers.
Nonperturbative Quantum Gravity
hep-th 2012-03 conditional novelty 3.0 of 10

Causal Dynamical Triangulations, reviewed in full, produce a four-dimensional de Sitter-like phase whose second-order boundary is presented as a candidate ultraviolet fixed point for quantum gravity.

How the literature uses it

6 arXiv papers cite this in 7 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Builds on it 1 paper

The spectral dimension of colored rooted $(D+1)$-ary trees is a simple extension of the result in [ref] .

$(D+1)$-Colored Graphs - a Review of Sundry Properties · Spectral dimension · 1.00

Cites it as background 2 papers

The spectral dimension of various classes of graphs has been studied by probabilists [ref] and by physicists, especially in the quantum gravity literature, see e.g. [ref] .

Spectral dimension of trees with a unique infinite spine · Introduction · 0.99
For example, a number of results are known about the Hausdorff dimension $d_H$ [ref] and spectral dimension $d_S$ [ref] of BP.

Phase Transition in Dually Weighted Colored Tensor Models · Comparison to branched polymers · 0.83

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