Properties of Quantum Graphity at Low Temperature

Fotini Markopoulou; Francesco Caravelli

RECORD

Properties of Quantum Graphity at Low Temperature

General Relativity and Quantum Cosmology · Submitted 7 Aug 2010

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

The authors' main claim Using mean field theory we find that an order parameter for the model is the average valence of the graph.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,914 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.24 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We present a mapping of dynamical graphs and, in particular, the graphs used in the Quantum Graphity models for emergent geometry, into an Ising hamiltonian on the line graph of a complete graph with a fixed number of vertices. We use this method to study the properties of Quantum Graphity models at low temperature in the limit in which the valence coupling constant of the model is much greater than the coupling constants of the loop terms. Using mean field theory we find that an order parameter for the model is the average valence of the graph. We calculate the equilibrium distribution for the valence as an implicit function of the temperature. In the approximation in which the temperature is low, we find the first two Taylor coefficients of the valence in the temperature expansion. A discussion of the susceptibility function and a generalization of the model are given in the end.

background contribution method result interpretation main claim

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	We present a mapping of dynamical graphs and, in particular, the graphs used in the Quantum Graphity models for emergent geometry, into an Ising hamiltonian on the line graph of a complete graph with a fixed number of vertices.	contribution 0.56	0.93	0.10	asserted 1.00
s1	We use this method to study the properties of Quantum Graphity models at low temperature in the limit in which the valence coupling constant of the model is much greater than the coupling constants of the loop terms.	contribution 0.61	0.92	0.06	asserted 0.95
s2	Using mean field theory we find that an order parameter for the model is the average valence of the graph.	result 0.98	0.96	0.33	asserted 1.00
s3	We calculate the equilibrium distribution for the valence as an implicit function of the temperature.	result 0.80	0.96	0.12	asserted 1.00
s4	In the approximation in which the temperature is low, we find the first two Taylor coefficients of the valence in the temperature expansion.	result 0.98	0.97	0.14	asserted 1.00
s5	A discussion of the susceptibility function and a generalization of the model are given in the end.	contribution 0.81	0.78	0.05	asserted 0.76

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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

We present a mapping of dynamical graphs and, in particular, the graphs used in the Quantum Graphity models for emergent geometry, into an Ising hamiltonian on the line graph of a complete graph with a fixed number of vertices. We use this method to study the properties of Quantum Graphity models at low temperature in the limit in which the valence coupling constant of the model is much greater than the coupling constants of the loop terms. Using mean field theory we find that an order parameter for the model is the average valence of the graph. We calculate the equilibrium distribution for the valence as an implicit function of the temperature. In the approximation in which the temperature is low, we find the first two Taylor coefficients of the valence in the temperature expansion. A discussion of the susceptibility function and a generalization of the model are given in the end.

Human review

How Pith checks papers → · Full audit of this paper →

References

How the literature uses it

6 arXiv papers cite this in 9 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 · 5 sentences without a confident label

Uses its method or tool 1 paper

This can be done by mapping $K_N$ to its line graph $L(K_N)$, as follows [ref] : Every edge of $K_N$ maps to a vertex in $L(K_N)$.

Background independent condensed matter models for quantum gravity · From a dynamical to a fixed lattice · 0.93

Cites it as background 1 paper

The setup is close in spirit to earlier models of quantum graphity explored by Konopka, Markopoulou, Smolin and others [ref] – [ref] .

Space as a low-temperature regime of graphs · Introduction · 0.92

What it cites · 8 sentences without a confident label

Builds on 1 paper

Following this work, in [ref] , we used the same concept of locality in terms of a dynamical lattice, but with a new type of matter that interacts non-linearly with the geometry, a precursor of gravity, and initiated a study of the quantum properties of that system.

A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime · Introduction · 0.97

Cites as support 1 paper

In fact, as shown in [ref] using the Lieb-Robinson bound, the speed with which information can propagate on graphs is bounded by a valence-dependent quantity.

Lieb-Robinson bounds for commutator-bounded operators · Conclusions · 0.97

Cites as background 4 papers

Dynamics in Quantum Graphity is given by a hamiltonian acting on the graph states of the form [ref] : [equation] where $H_V$ keeps track of how many on edges are attached to a single vertex, and $H_L$ counts closed paths in the graph.

Quantum Graphity · Quantum Graphity · 0.81
Wen's work on emergent matter and gravitons from a bosonic spin system [ref] , the emergence of a Lorentzian metric and aspects of gravitation such as Hawking radiation in analog models of gravity [ref] , as well as long-standing approaches such as matrix models [ref] , and more radical formulations of geometry in terms of information [ref] .

Dumb Holes and the Effects of High Frequencies on Black Hole Evaporation · Introduction · 1.00
Wen's work on emergent matter and gravitons from a bosonic spin system [ref] , the emergence of a Lorentzian metric and aspects of gravitation such as Hawking radiation in analog models of gravity [ref] , as well as long-standing approaches such as matrix models [ref] , and more radical formulations of geometry in terms of information [ref] .

Emergent Spacetime · Introduction · 1.00

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.