Infinite-Volume Gibbs States of the Generalized Mean-Field Orthoplicial Model.
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| Title: | Infinite-Volume Gibbs States of the Generalized Mean-Field Orthoplicial Model. |
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| Authors: | Koskinen, Kalle1 (AUTHOR) kalle.koskinen@helsinki.fi |
| Source: | Journal of Statistical Physics. Sep2024, Vol. 191 Issue 9, p1-44. 44p. |
| Subjects: | Statistical equilibrium, Probability measures, Statistical mechanics, Partition functions, Integral representations |
| Abstract: | The generalized mean-field orthoplicial model is a mean-field model on a space of continuous spins on R n that are constrained to a scaled (n - 1) -dimensional ℓ 1 -sphere, equivalently a scaled (n - 1) -dimensional orthoplex, and interact through a general interaction function. The finite-volume Gibbs states of this model correspond to singular probability measures. In this paper, we use probabilistic methods to rigorously classify the infinite-volume Gibbs states of this model, and we show that they are convex combinations of product states. The predominant methods utilize the theory of large deviations, relative entropy, and equivalence of ensembles, and the key technical tools utilize exact integral representations of certain partition functions and locally uniform estimates of expectations of certain local observables. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 179278026 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Infinite-Volume Gibbs States of the Generalized Mean-Field Orthoplicial Model. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Koskinen%2C+Kalle%22">Koskinen, Kalle</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kalle.koskinen@helsinki.fi</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Statistical+Physics%22">Journal of Statistical Physics</searchLink>. Sep2024, Vol. 191 Issue 9, p1-44. 44p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Statistical+equilibrium%22">Statistical equilibrium</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+measures%22">Probability measures</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+mechanics%22">Statistical mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Partition+functions%22">Partition functions</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+representations%22">Integral representations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The generalized mean-field orthoplicial model is a mean-field model on a space of continuous spins on R n that are constrained to a scaled (n - 1) -dimensional ℓ 1 -sphere, equivalently a scaled (n - 1) -dimensional orthoplex, and interact through a general interaction function. The finite-volume Gibbs states of this model correspond to singular probability measures. In this paper, we use probabilistic methods to rigorously classify the infinite-volume Gibbs states of this model, and we show that they are convex combinations of product states. The predominant methods utilize the theory of large deviations, relative entropy, and equivalence of ensembles, and the key technical tools utilize exact integral representations of certain partition functions and locally uniform estimates of expectations of certain local observables. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Statistical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10955-024-03321-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 44 StartPage: 1 Subjects: – SubjectFull: Statistical equilibrium Type: general – SubjectFull: Probability measures Type: general – SubjectFull: Statistical mechanics Type: general – SubjectFull: Partition functions Type: general – SubjectFull: Integral representations Type: general Titles: – TitleFull: Infinite-Volume Gibbs States of the Generalized Mean-Field Orthoplicial Model. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Koskinen, Kalle IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 00224715 Numbering: – Type: volume Value: 191 – Type: issue Value: 9 Titles: – TitleFull: Journal of Statistical Physics Type: main |
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