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Functional order parameters for the quenched free energy 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 Under the assumption that the two order parameters can be chosen to be the same, in the thermodynamic limit, it is shown that the Parisi free energy is a rigorous upper bound for the free energy of the model.

how it is stated · asserted 0.99 read the record →

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arXiv ID1212.2913 (version 1)
Pith IDGIOGR65Z, Pith's permanent record of this paper and its review
CitationFrancesco Guerra. "Functional order parameters for the quenched free energy in mean field spin glass models." arXiv:1212.2913 (2012). https://pith.science/paper/GIOGR65Z
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,030 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.70 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.69 · compares with prior results 0.92 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In the Sherrington-Kirkpatrick mean field model for spin glasses, we show that the quenched average of the free energy can be expressed through a couple of functional order parameters, in a form very similar to the one found in the frame of the replica symmetry breaking method. The functional order parameters are implicitely given in terms of fluctuations of thermodynamic variables. Under the assumption that the two order parameters can be chosen to be the same, in the thermodynamic limit, it is shown that the Parisi free energy is a rigorous upper bound for the free energy of the model.

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 In the Sherrington-Kirkpatrick mean field model for spin glasses, we show that the quenched average of the free energy can be expressed through a couple of functional order parameters, in a form very similar to the one found in the frame of the replica symmetry breaking method. result 0.64 0.94 0.69 asserted 1.00
s1 The functional order parameters are implicitely given in terms of fluctuations of thermodynamic variables. result 0.52 0.80 0.07 asserted 1.00
s2 Under the assumption that the two order parameters can be chosen to be the same, in the thermodynamic limit, it is shown that the Parisi free energy is a rigorous upper bound for the free energy of the model. result 0.98 0.88 0.52 asserted 0.99

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

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  • references and citing 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

In the Sherrington-Kirkpatrick mean field model for spin glasses, we show that the quenched average of the free energy can be expressed through a couple of functional order parameters, in a form very similar to the one found in the frame of the replica symmetry breaking method. The functional order parameters are implicitely given in terms of fluctuations of thermodynamic variables. Under the assumption that the two order parameters can be chosen to be the same, in the thermodynamic limit, it is shown that the Parisi free energy is a rigorous upper bound for the free energy of the model.

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