Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model

Denjoe O'Connor; Julieta Medina; Wolfgang Bietenholz

RECORD

Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model

Julieta Medina, Wolfgang Bietenholz, Denjoe O'Connor

High Energy Physics - Theory · Submitted 20 Dec 2007

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

The authors' main claim Thus we identify the phases of disorder, uniform order and non-uniform order.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID0712.3366 (version 1)

Pith IDLA5CEC3Q, Pith's permanent record of this paper and its review

CitationDenjoe O'Connor, Julieta Medina, Wolfgang Bietenholz. "Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model." arXiv:0712.3366 (2007). https://pith.science/paper/LA5CEC3Q

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, 6,734 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.27 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We regularise the 3d \lambda \phi^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical harmonics. This yields a numerically tractable formulation, which constitutes an unconventional alternative to the lattice. In contrast to the 2d version, the radius R plays an independent r\^{o}le. We explore the phase diagram in terms of R and the cutoff, as well as the parameters m^2 and \lambda. Thus we identify the phases of disorder, uniform order and non-uniform order. We compare the result to the phase diagrams of the 3d model on a non-commutative torus, and of the 2d model on a fuzzy sphere. Our data at strong coupling reproduce accurately the behaviour of a matrix chain, which corresponds to the c=1-model in string theory. This observation enables a conjecture about the thermodynamic limit.

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 regularise the 3d \lambda \phi^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere.	method 0.94	0.94	0.04	asserted 1.00
s1	The latter involves a truncated expansion of the field in spherical harmonics.	method 1.00	0.40	0.02	asserted 1.00
s2	This yields a numerically tractable formulation, which constitutes an unconventional alternative to the lattice.	method 0.59	0.65	0.08	asserted 1.00
s3	In contrast to the 2d version, the radius R plays an independent r\^{o}le.	method 0.30	0.29	0.04	asserted 1.00
s4	We explore the phase diagram in terms of R and the cutoff, as well as the parameters m^2 and \lambda.	contribution 0.61	0.92	0.05	asserted 0.97
s5	Thus we identify the phases of disorder, uniform order and non-uniform order.	result 0.99	0.94	0.22	asserted 1.00
s6	We compare the result to the phase diagrams of the 3d model on a non-commutative torus, and of the 2d model on a fuzzy sphere.	contribution 0.58	0.70	0.06	asserted 0.95
s7	Our data at strong coupling reproduce accurately the behaviour of a matrix chain, which corresponds to the c=1-model in string theory.	result 0.98	0.91	0.20	asserted 1.00
s8	This observation enables a conjecture about the thermodynamic limit.	interpretation 0.99	0.56	0.31	hedged possibility 0.35

What kind of paper the classifier reports this is: simulation study 0.99 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

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 regularise the 3d \lambda \phi^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical harmonics. This yields a numerically tractable formulation, which constitutes an unconventional alternative to the lattice. In contrast to the 2d version, the radius R plays an independent r\^{o}le. We explore the phase diagram in terms of R and the cutoff, as well as the parameters m^2 and \lambda. Thus we identify the phases of disorder, uniform order and non-uniform order. We compare the result to the phase diagrams of the 3d model on a non-commutative torus, and of the 2d model on a fuzzy sphere. Our data at strong coupling reproduce accurately the behaviour of a matrix chain, which corresponds to the c=1-model in string theory. This observation enables a conjecture about the thermodynamic limit.

Human review

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

How the literature uses it

17 arXiv papers cite this in 22 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We evaluate the phase diagram, where we find a disordered phase and an ordered regime, which splits into phases of uniform and non-uniform order.

Field Theory Simulations on a Fuzzy Sphere - an Alternative to the Lattice · 0.95

Papers citing it · 12 sentences without a confident label

Contests it 1 paper

This should be contrasted with the Monte Carlo simulation (via Metropolis, Hybrid Monte Carlo or other method) of ([ref]) which suffers from severe ergodic problems which do not allow us easy and transparent access to the stripe transition and the triple point [ref] .

Phase diagrams of the multitrace quartic matrix models of noncommutative \Phi^4 · Introduction · contest 0.81

Compares with it 2 papers

This did not have to happen and in fact the corresponding lines do not all collapse together for a related three dimensional model [ref] , where the spacetime is taken to be a fuzzy sphere direct producted with a temporal direction.

Simulation of a scalar field on a fuzzy sphere · Conclusions · 0.97
This diagram structure is also found in matrix models on other NC spaces such as the fuzzy sphere [ref] , the fuzzy disc [ref] , and the fuzzy complex projective space [ref] .

Phase transitions in a $\Phi^4$ matrix model on a curved noncommutative space · Phase diagram · 0.86

Cites it as support 1 paper

For example we can show in a particular double scaling limit that the nonperturbative phase structure of scalar fields on the Moyal-Weyl plane can be rigorously identified with the nonperturbative phase structure of scalar fields on the fuzzy sphere, and in particular the matrix or nonuniform ordered phase on the fuzzy sphere goes precisely to the stripe phase on the Moyal-Weyl plane [ref] .

Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models · Introduction · 0.97

Cites it as background 6 papers

This problem was also studied in [ref] .

New Algorithm and Phase Diagram of Noncommutative Phi**4 on the Fuzzy Sphere · Introduction · 0.87
The problem of the phase structure of fuzzy scalar phi-four was also studied by means of the Monte Carlo method in [ref] .

Phase diagrams of the multitrace quartic matrix models of noncommutative \Phi^4 · Introduction · 0.93
The problem of the phase structure of fuzzy scalar phi-four was also studied in [ref] .

A Multitrace Approach to Noncommutative \Phi_2^4 · Introduction · 0.99

What it cites · 3 sentences without a confident label

Builds on 2 papers

So far the 2d $λϕ^4$ model has been investigated in this respect [ref] .[Further numerical studies on the fuzzy sphere address $U(1)$ gauge theory [ref] .] Here we extend this study to three dimensions, where the spatial plane is mapped onto a fuzzy sphere, and the Euclidean time is lattice discretised.

Finite temperature phase transition of a single scalar field on a fuzzy sphere · Introduction · 0.99
So far the 2d $λϕ^4$ model has been investigated in this respect [ref] .[Further numerical studies on the fuzzy sphere address $U(1)$ gauge theory [ref] .] Here we extend this study to three dimensions, where the spatial plane is mapped onto a fuzzy sphere, and the Euclidean time is lattice discretised.

Geometry in transition: A model of emergent geometry · Introduction · 0.99

Uses the method or tool of 1 paper

Equivalent tools were applied before in investigations of the 2d model on a fuzzy sphere [ref] .

Finite temperature phase transition of a single scalar field on a fuzzy sphere · Observables · 0.84

Compares with 1 paper

We found, however, significant differences from the 2d $λϕ^4$ model an a fuzzy sphere [ref] .

Finite temperature phase transition of a single scalar field on a fuzzy sphere · Conclusions · 0.99

Cites as background 2 papers

We are going to see that this property can indeed affect the thermodynamic limit.[The impact of a non-local regularisation on the continuum limit is intensively discussed in the lattice community (see e.g. Refs. [ref] ) in particular in the light of recent large-scale QCD simulations with “rooted staggered fermions”. ]

Why rooting fails · Regularisation · 0.89
This virtue may prove particularly powerful in cases where continuous rotational and translational symmetry (which we obtain in the large $R$ limit) play a central rôle, such as supersymmetric models.[Literature on supersymmetric systems on a fuzzy sphere exists regarding the theoretical basis [ref] and first simulations [ref] , though there are many outstanding issues in that field.

Notes on noncommutative supersymmetric gauge theory on the fuzzy supersphere · Regularisation · 0.83

Discussion

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