Pre-logarithmic and logarithmic fields in a sandpile model

Geoffroy Piroux; Philippe Ruelle

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Pre-logarithmic and logarithmic fields in a sandpile model

Geoffroy Piroux, Philippe Ruelle

High Energy Physics - Theory · Submitted 16 Jul 2004

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

The authors' main claim We show that the scaling limit of the mass insertion operator is a weight zero logarithmic field.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,707 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.91 · compares with prior results 0.81 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We consider the unoriented two-dimensional Abelian sandpile model on the half-plane with open and closed boundary conditions, and relate it to the boundary logarithmic conformal field theory with central charge c=-2. Building on previous results, we first perform a complementary lattice analysis of the operator effecting the change of boundary condition between open and closed, which confirms that this operator is a weight -1/8 boundary primary field, whose fusion agrees with lattice calculations. We then consider the operators corresponding to the unit height variable and to a mass insertion at an isolated site of the upper half plane and compute their one-point functions in presence of a boundary containing the two kinds of boundary conditions. We show that the scaling limit of the mass insertion operator is a weight zero logarithmic field.

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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	We consider the unoriented two-dimensional Abelian sandpile model on the half-plane with open and closed boundary conditions, and relate it to the boundary logarithmic conformal field theory with central charge c=-2.	contribution 0.83	0.82	0.21	asserted 1.00
s1	Building on previous results, we first perform a complementary lattice analysis of the operator effecting the change of boundary condition between open and closed, which confirms that this operator is a weight -1/8 boundary primary field, whose fusion agrees with lattice calculations.	contribution 0.51	0.91	0.10	asserted 1.00
s2	We then consider the operators corresponding to the unit height variable and to a mass insertion at an isolated site of the upper half plane and compute their one-point functions in presence of a boundary containing the two kinds of boundary conditions.	contribution 0.92	0.94	0.05	asserted 0.84
s3	We show that the scaling limit of the mass insertion operator is a weight zero logarithmic field.	result 1.00	0.94	0.42	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.64.

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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

We consider the unoriented two-dimensional Abelian sandpile model on the half-plane with open and closed boundary conditions, and relate it to the boundary logarithmic conformal field theory with central charge c=-2. Building on previous results, we first perform a complementary lattice analysis of the operator effecting the change of boundary condition between open and closed, which confirms that this operator is a weight -1/8 boundary primary field, whose fusion agrees with lattice calculations. We then consider the operators corresponding to the unit height variable and to a mass insertion at an isolated site of the upper half plane and compute their one-point functions in presence of a boundary containing the two kinds of boundary conditions. We show that the scaling limit of the mass insertion operator is a weight zero logarithmic field.

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References

Forward citations

Cited by 2 Pith papers

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

Logarithmic correlation functions for critical dense polymers on the cylinder
cond-mat.stat-mech 2019-07 unverdicted novelty 7.0 of 10

Explicit finite-n lattice correlators for dense polymers on a cylinder are computed via Temperley-Lieb algebra and shown to match ratios of c=-2 CFT correlators involving boundary fields of dimensions -1/8 and 0, with...
Holographic applications of logarithmic conformal field theories
hep-th 2013-02 accept novelty 3.0 of 10

Critically tuned anti-de Sitter gravity theories are conjectured to be dual to logarithmic conformal field theories, and this review assembles the correlator and partition-function evidence for that correspondence.

How the literature uses it

4 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 · 2 sentences without a confident label

Compares with it 1 paper

Interestingly, comparing with the results of [ref] , we see that the values of $a$ and $b$ are different, but that the relation $b = - a^2/4$ is the same, leading us to wonder whether this is a universal feature of logarithmic CFTs at $c=-2$.

Logarithmic correlation functions for critical dense polymers on the cylinder · Analysis for the fields $ω(z)$ · 0.97

Cites it as support 1 paper

According to [ref] , the OPE of $μ$ operator is the direct sum of identity operator and its logarithmic partner and the second one corresponds to the sink point which is our case.

Numerical Determination of Boundary Condition Changing Operators · Calculation of $ρ$ · 0.96

Cites it as background 2 papers

Logarithms in correlation functions were previously found in various lattice models, including the abelian sandpile model [ref] , critical dense polymers [ref] , critical percolation [ref] and the $Q$-state Potts model [ref] .

Logarithmic correlation functions for critical dense polymers on the cylinder · Introduction · 0.80
Log CFTs have appeared in a number of different contexts in condensed matter physics and related subjects, like 2-dimensional turbulence [ref] (see also [ref] ), abelian sandpile models [ref] , critical polymers [ref] , D-brane recoil [ref] or decay [ref] , fractional quantum-Hall effect [ref] , gravitational dressing [ref] , percolation [ref] , symplectic fermions [ref] , and systems with disorder [ref] or quenched disorder [ref] .

Holographic applications of logarithmic conformal field theories · Condensed matter applications · 0.94

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