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The Extended Variational Principle for Mean-Field, Classical Spin Systems

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Eugene Kritchevski, Shannon Starr

Mathematical Physics · Submitted 30 Apr 2005

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

The authors' main claim This is a new connection, and it permits a generalization of the EVP.

how it is stated · asserted 0.99 read the record →

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arXiv IDmath-ph/0505001 (version 1)
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CitationEugene Kritchevski, Shannon Starr. "The Extended Variational Principle for Mean-Field, Classical Spin Systems." arXiv:math-ph/0505001 (2005). https://pith.science/paper/ILB4ZOMF
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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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,023 input tokens.

What the abstract itself states, as probabilities: claims first 0.18 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.02 · states quantitative result 0.03 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The purpose of this article is to obtain a better understanding of the extended variational principle (EVP). The EVP is a formula for the thermodynamic pressure of a statistical mechanical system as a limit of a sequence of minimization problems. It was developed for disordered mean-field spin systems, spin systems where the underlying Hamiltonian is itself random, and whose distribution is permutation invariant. We present the EVP in the simpler setting of classical mean-field spin systems, where the Hamiltonian is non-random and symmetric. The EVP essentially solves these models. We compare the EVP with another method for mean-field spin systems: the self-consistent mean-field equations. The two approaches lead to dual convex optimization problems. This is a new connection, and it permits a generalization of the EVP.

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 The purpose of this article is to obtain a better understanding of the extended variational principle (EVP). contribution 0.53 0.39 0.04 asserted 0.77
s1 The EVP is a formula for the thermodynamic pressure of a statistical mechanical system as a limit of a sequence of minimization problems. background 1.00 0.10 0.06 asserted 1.00
s2 It was developed for disordered mean-field spin systems, spin systems where the underlying Hamiltonian is itself random, and whose distribution is permutation invariant. background 1.00 0.07 0.03 asserted 1.00
s3 We present the EVP in the simpler setting of classical mean-field spin systems, where the Hamiltonian is non-random and symmetric. contribution 0.84 0.86 0.07 asserted 0.99
s4 The EVP essentially solves these models. interpretation 0.60 0.31 0.33 asserted 0.99
s5 We compare the EVP with another method for mean-field spin systems: the self-consistent mean-field equations. contribution 0.67 0.74 0.05 asserted 0.97
s6 The two approaches lead to dual convex optimization problems. result 0.90 0.76 0.14 asserted 1.00
s7 This is a new connection, and it permits a generalization of the EVP. contribution 0.39 0.86 0.33 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 0.93.

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

The purpose of this article is to obtain a better understanding of the extended variational principle (EVP). The EVP is a formula for the thermodynamic pressure of a statistical mechanical system as a limit of a sequence of minimization problems. It was developed for disordered mean-field spin systems, spin systems where the underlying Hamiltonian is itself random, and whose distribution is permutation invariant. We present the EVP in the simpler setting of classical mean-field spin systems, where the Hamiltonian is non-random and symmetric. The EVP essentially solves these models. We compare the EVP with another method for mean-field spin systems: the self-consistent mean-field equations. The two approaches lead to dual convex optimization problems. This is a new connection, and it permits a generalization of the EVP.

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