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About the overlap distribution in mean field spin glass models

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Francesco Guerra

Disordered Systems and Neural Networks · Submitted 12 Dec 2012

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

The authors' main claim They are in full agreement with the Parisi accepted picture of spontaneous replica symmetry breaking.

how it is stated · asserted 0.96 read the record →

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arXiv ID1212.2919 (version 1)
Pith IDGPF42YT7, Pith's permanent record of this paper and its review
CitationFrancesco Guerra. "About the overlap distribution in mean field spin glass models." arXiv:1212.2919 (2012). https://pith.science/paper/GPF42YT7
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,813 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.88 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. Here we establish some properties of the distribution of overlaps between real replicas. They are in full agreement with the Parisi accepted picture of spontaneous replica symmetry breaking. As a byproduct, we show that the selfaveraging of the Edwards-Anderson fluctuating order parameter, with respect to the external quenched noise, implies that the overlap distribution is given by the Sherrington-Kirkpatrick replica symmetric Ansatz. This extends previous results of Pastur and Shcherbina. Finally, we show how to generalize our results to realistic short range spin glass models.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. background 0.92 0.56 0.04 asserted 0.68
s1 Here we establish some properties of the distribution of overlaps between real replicas. contribution 0.97 0.93 0.29 asserted 0.99
s2 They are in full agreement with the Parisi accepted picture of spontaneous replica symmetry breaking. interpretation 0.93 0.49 0.30 asserted 0.96
s3 As a byproduct, we show that the selfaveraging of the Edwards-Anderson fluctuating order parameter, with respect to the external quenched noise, implies that the overlap distribution is given by the Sherrington-Kirkpatrick replica symmetric Ansatz. result 0.97 0.91 0.26 asserted 1.00
s4 This extends previous results of Pastur and Shcherbina. background 0.63 0.35 0.04 asserted 0.98
s5 Finally, we show how to generalize our results to realistic short range spin glass models. contribution 0.59 0.90 0.08 asserted 1.00

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

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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 continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. Here we establish some properties of the distribution of overlaps between real replicas. They are in full agreement with the Parisi accepted picture of spontaneous replica symmetry breaking. As a byproduct, we show that the selfaveraging of the Edwards-Anderson fluctuating order parameter, with respect to the external quenched noise, implies that the overlap distribution is given by the Sherrington-Kirkpatrick replica symmetric Ansatz. This extends previous results of Pastur and Shcherbina. Finally, we show how to generalize our results to realistic short range spin glass models.

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