Forbidden Gap Argument for Phase Transitions Proved by Means of Chessboard Estimates

Abstract Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the e...
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Autor*in:	Biskup, Marek [verfasserIn] Kotecký, Roman

Format:	Artikel
Sprache:	Englisch

Erschienen:	2006

Schlagwörter:	Neural Network Phase Transition Statistical Physic Phase Diagram Complex System

Anmerkung:	© Springer-Verlag Berlin Heidelberg 2006

Übergeordnetes Werk:	Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 264(2006), 3 vom: 22. März, Seite 631-656
Übergeordnetes Werk:	volume:264 ; year:2006 ; number:3 ; day:22 ; month:03 ; pages:631-656

Links:	Volltext

DOI / URN:	10.1007/s00220-006-1523-x

Katalog-ID:	OLC2038889147

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520			\|a Abstract Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the existence of shift-ergodic states that differ significantly from those proved to exist. For models depending on a parameter (say, the temperature), this shows that the values of the conjugate thermodynamic quantity (the energy) inside the ``transitional gap'' are forbidden in all shift-ergodic Gibbs states. We point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria.
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allfields	10.1007/s00220-006-1523-x doi (DE-627)OLC2038889147 (DE-He213)s00220-006-1523-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Biskup, Marek verfasserin aut Forbidden Gap Argument for Phase Transitions Proved by Means of Chessboard Estimates 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2006 Abstract Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the existence of shift-ergodic states that differ significantly from those proved to exist. For models depending on a parameter (say, the temperature), this shows that the values of the conjugate thermodynamic quantity (the energy) inside the ``transitional gap'' are forbidden in all shift-ergodic Gibbs states. We point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria. Neural Network Phase Transition Statistical Physic Phase Diagram Complex System Kotecký, Roman aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 264(2006), 3 vom: 22. März, Seite 631-656 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:264 year:2006 number:3 day:22 month:03 pages:631-656 https://doi.org/10.1007/s00220-006-1523-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 264 2006 3 22 03 631-656
spelling	10.1007/s00220-006-1523-x doi (DE-627)OLC2038889147 (DE-He213)s00220-006-1523-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Biskup, Marek verfasserin aut Forbidden Gap Argument for Phase Transitions Proved by Means of Chessboard Estimates 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2006 Abstract Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the existence of shift-ergodic states that differ significantly from those proved to exist. For models depending on a parameter (say, the temperature), this shows that the values of the conjugate thermodynamic quantity (the energy) inside the ``transitional gap'' are forbidden in all shift-ergodic Gibbs states. We point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria. Neural Network Phase Transition Statistical Physic Phase Diagram Complex System Kotecký, Roman aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 264(2006), 3 vom: 22. März, Seite 631-656 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:264 year:2006 number:3 day:22 month:03 pages:631-656 https://doi.org/10.1007/s00220-006-1523-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 264 2006 3 22 03 631-656
allfields_unstemmed	10.1007/s00220-006-1523-x doi (DE-627)OLC2038889147 (DE-He213)s00220-006-1523-x-p DE-627 ger DE-627 rakwb eng 530 510 VZ Biskup, Marek verfasserin aut Forbidden Gap Argument for Phase Transitions Proved by Means of Chessboard Estimates 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2006 Abstract Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the existence of shift-ergodic states that differ significantly from those proved to exist. For models depending on a parameter (say, the temperature), this shows that the values of the conjugate thermodynamic quantity (the energy) inside the ``transitional gap'' are forbidden in all shift-ergodic Gibbs states. We point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria. Neural Network Phase Transition Statistical Physic Phase Diagram Complex System Kotecký, Roman aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 264(2006), 3 vom: 22. März, Seite 631-656 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:264 year:2006 number:3 day:22 month:03 pages:631-656 https://doi.org/10.1007/s00220-006-1523-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 264 2006 3 22 03 631-656
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title_sort	forbidden gap argument for phase transitions proved by means of chessboard estimates
title_auth	Forbidden Gap Argument for Phase Transitions Proved by Means of Chessboard Estimates
abstract	Abstract Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the existence of shift-ergodic states that differ significantly from those proved to exist. For models depending on a parameter (say, the temperature), this shows that the values of the conjugate thermodynamic quantity (the energy) inside the ``transitional gap'' are forbidden in all shift-ergodic Gibbs states. We point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria. © Springer-Verlag Berlin Heidelberg 2006
abstractGer	Abstract Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the existence of shift-ergodic states that differ significantly from those proved to exist. For models depending on a parameter (say, the temperature), this shows that the values of the conjugate thermodynamic quantity (the energy) inside the ``transitional gap'' are forbidden in all shift-ergodic Gibbs states. We point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria. © Springer-Verlag Berlin Heidelberg 2006
abstract_unstemmed	Abstract Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the existence of shift-ergodic states that differ significantly from those proved to exist. For models depending on a parameter (say, the temperature), this shows that the values of the conjugate thermodynamic quantity (the energy) inside the ``transitional gap'' are forbidden in all shift-ergodic Gibbs states. We point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria. © Springer-Verlag Berlin Heidelberg 2006
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title_short	Forbidden Gap Argument for Phase Transitions Proved by Means of Chessboard Estimates
url	https://doi.org/10.1007/s00220-006-1523-x
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author2	Kotecký, Roman
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doi_str	10.1007/s00220-006-1523-x
up_date	2024-07-03T20:44:21.885Z
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