General properties of polymer systems

Abstract We prove the existence of the thermodynamic limit for the pressure and show that the limit is a convex, continuous function of the chemical potential. The existence and analyticity properties of the thermodynamic limit for the correlation functions is then derived; we discuss in particular...
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Gespeichert in:

Autor*in:	Gruber, C. [verfasserIn] Kunz, H.

Format:	Artikel
Sprache:	Englisch

Erschienen:	1971

Schlagwörter:	Polymer Neural Network Phase Transition Statistical Physic Continuous Function

Anmerkung:	© Springer-Verlag 1971

Übergeordnetes Werk:	Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 22(1971), 2 vom: Juni, Seite 133-161
Übergeordnetes Werk:	volume:22 ; year:1971 ; number:2 ; month:06 ; pages:133-161

Links:	Volltext

DOI / URN:	10.1007/BF01651334

Katalog-ID:	OLC2038824002

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allfields	10.1007/BF01651334 doi (DE-627)OLC2038824002 (DE-He213)BF01651334-p DE-627 ger DE-627 rakwb eng 530 510 VZ Gruber, C. verfasserin aut General properties of polymer systems 1971 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1971 Abstract We prove the existence of the thermodynamic limit for the pressure and show that the limit is a convex, continuous function of the chemical potential. The existence and analyticity properties of the thermodynamic limit for the correlation functions is then derived; we discuss in particular the Mayer Series and the virial expansion. In the special case of Monomer-Dimer systems it is established that no phase transition is possible; moreover it is shown that the Mayer Series for the density is a series of Stieltjes, which yields upper and lower bounds in terms of Padé approximants. Finally it is shown that the results obtained for polymer systems can be used to study classical lattice systems. Polymer Neural Network Phase Transition Statistical Physic Continuous Function Kunz, H. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 22(1971), 2 vom: Juni, Seite 133-161 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:22 year:1971 number:2 month:06 pages:133-161 https://doi.org/10.1007/BF01651334 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_130 GBV_ILN_170 GBV_ILN_201 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4125 GBV_ILN_4193 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 22 1971 2 06 133-161
spelling	10.1007/BF01651334 doi (DE-627)OLC2038824002 (DE-He213)BF01651334-p DE-627 ger DE-627 rakwb eng 530 510 VZ Gruber, C. verfasserin aut General properties of polymer systems 1971 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1971 Abstract We prove the existence of the thermodynamic limit for the pressure and show that the limit is a convex, continuous function of the chemical potential. The existence and analyticity properties of the thermodynamic limit for the correlation functions is then derived; we discuss in particular the Mayer Series and the virial expansion. In the special case of Monomer-Dimer systems it is established that no phase transition is possible; moreover it is shown that the Mayer Series for the density is a series of Stieltjes, which yields upper and lower bounds in terms of Padé approximants. Finally it is shown that the results obtained for polymer systems can be used to study classical lattice systems. Polymer Neural Network Phase Transition Statistical Physic Continuous Function Kunz, H. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 22(1971), 2 vom: Juni, Seite 133-161 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:22 year:1971 number:2 month:06 pages:133-161 https://doi.org/10.1007/BF01651334 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_130 GBV_ILN_170 GBV_ILN_201 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4125 GBV_ILN_4193 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 22 1971 2 06 133-161
allfields_unstemmed	10.1007/BF01651334 doi (DE-627)OLC2038824002 (DE-He213)BF01651334-p DE-627 ger DE-627 rakwb eng 530 510 VZ Gruber, C. verfasserin aut General properties of polymer systems 1971 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1971 Abstract We prove the existence of the thermodynamic limit for the pressure and show that the limit is a convex, continuous function of the chemical potential. The existence and analyticity properties of the thermodynamic limit for the correlation functions is then derived; we discuss in particular the Mayer Series and the virial expansion. In the special case of Monomer-Dimer systems it is established that no phase transition is possible; moreover it is shown that the Mayer Series for the density is a series of Stieltjes, which yields upper and lower bounds in terms of Padé approximants. Finally it is shown that the results obtained for polymer systems can be used to study classical lattice systems. Polymer Neural Network Phase Transition Statistical Physic Continuous Function Kunz, H. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 22(1971), 2 vom: Juni, Seite 133-161 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:22 year:1971 number:2 month:06 pages:133-161 https://doi.org/10.1007/BF01651334 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_130 GBV_ILN_170 GBV_ILN_201 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4125 GBV_ILN_4193 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 22 1971 2 06 133-161
allfieldsGer	10.1007/BF01651334 doi (DE-627)OLC2038824002 (DE-He213)BF01651334-p DE-627 ger DE-627 rakwb eng 530 510 VZ Gruber, C. verfasserin aut General properties of polymer systems 1971 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1971 Abstract We prove the existence of the thermodynamic limit for the pressure and show that the limit is a convex, continuous function of the chemical potential. The existence and analyticity properties of the thermodynamic limit for the correlation functions is then derived; we discuss in particular the Mayer Series and the virial expansion. In the special case of Monomer-Dimer systems it is established that no phase transition is possible; moreover it is shown that the Mayer Series for the density is a series of Stieltjes, which yields upper and lower bounds in terms of Padé approximants. Finally it is shown that the results obtained for polymer systems can be used to study classical lattice systems. Polymer Neural Network Phase Transition Statistical Physic Continuous Function Kunz, H. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 22(1971), 2 vom: Juni, Seite 133-161 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:22 year:1971 number:2 month:06 pages:133-161 https://doi.org/10.1007/BF01651334 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_130 GBV_ILN_170 GBV_ILN_201 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4125 GBV_ILN_4193 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 22 1971 2 06 133-161
allfieldsSound	10.1007/BF01651334 doi (DE-627)OLC2038824002 (DE-He213)BF01651334-p DE-627 ger DE-627 rakwb eng 530 510 VZ Gruber, C. verfasserin aut General properties of polymer systems 1971 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1971 Abstract We prove the existence of the thermodynamic limit for the pressure and show that the limit is a convex, continuous function of the chemical potential. The existence and analyticity properties of the thermodynamic limit for the correlation functions is then derived; we discuss in particular the Mayer Series and the virial expansion. In the special case of Monomer-Dimer systems it is established that no phase transition is possible; moreover it is shown that the Mayer Series for the density is a series of Stieltjes, which yields upper and lower bounds in terms of Padé approximants. Finally it is shown that the results obtained for polymer systems can be used to study classical lattice systems. Polymer Neural Network Phase Transition Statistical Physic Continuous Function Kunz, H. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 22(1971), 2 vom: Juni, Seite 133-161 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:22 year:1971 number:2 month:06 pages:133-161 https://doi.org/10.1007/BF01651334 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_130 GBV_ILN_170 GBV_ILN_201 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4125 GBV_ILN_4193 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4700 AR 22 1971 2 06 133-161
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author	Gruber, C.
spellingShingle	Gruber, C. ddc 530 misc Polymer misc Neural Network misc Phase Transition misc Statistical Physic misc Continuous Function General properties of polymer systems
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topic_title	530 510 VZ General properties of polymer systems Polymer Neural Network Phase Transition Statistical Physic Continuous Function
topic	ddc 530 misc Polymer misc Neural Network misc Phase Transition misc Statistical Physic misc Continuous Function
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title	General properties of polymer systems
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title_full	General properties of polymer systems
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title_sort	general properties of polymer systems
title_auth	General properties of polymer systems
abstract	Abstract We prove the existence of the thermodynamic limit for the pressure and show that the limit is a convex, continuous function of the chemical potential. The existence and analyticity properties of the thermodynamic limit for the correlation functions is then derived; we discuss in particular the Mayer Series and the virial expansion. In the special case of Monomer-Dimer systems it is established that no phase transition is possible; moreover it is shown that the Mayer Series for the density is a series of Stieltjes, which yields upper and lower bounds in terms of Padé approximants. Finally it is shown that the results obtained for polymer systems can be used to study classical lattice systems. © Springer-Verlag 1971
abstractGer	Abstract We prove the existence of the thermodynamic limit for the pressure and show that the limit is a convex, continuous function of the chemical potential. The existence and analyticity properties of the thermodynamic limit for the correlation functions is then derived; we discuss in particular the Mayer Series and the virial expansion. In the special case of Monomer-Dimer systems it is established that no phase transition is possible; moreover it is shown that the Mayer Series for the density is a series of Stieltjes, which yields upper and lower bounds in terms of Padé approximants. Finally it is shown that the results obtained for polymer systems can be used to study classical lattice systems. © Springer-Verlag 1971
abstract_unstemmed	Abstract We prove the existence of the thermodynamic limit for the pressure and show that the limit is a convex, continuous function of the chemical potential. The existence and analyticity properties of the thermodynamic limit for the correlation functions is then derived; we discuss in particular the Mayer Series and the virial expansion. In the special case of Monomer-Dimer systems it is established that no phase transition is possible; moreover it is shown that the Mayer Series for the density is a series of Stieltjes, which yields upper and lower bounds in terms of Padé approximants. Finally it is shown that the results obtained for polymer systems can be used to study classical lattice systems. © Springer-Verlag 1971
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