Ising models, julia sets, and similarity of the maximal entropy measures

Abstract We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this mode...
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Autor*in:	Ishii, Yutaka

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	1995

Umfang:	11

Reproduktion:	Springer Online Journal Archives 1860-2002
Übergeordnetes Werk:	in: Journal of statistical physics - 1969, 78(1995) vom: März/Apr., Seite 815-825
Übergeordnetes Werk:	volume:78 ; year:1995 ; month:03/04 ; pages:815-825 ; extent:11

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Katalog-ID:	NLEJ197937977

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520			\|a Abstract We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this model is a rational endomorphism (denoted byf) of Ĉ and that the singularities of the free energy lie on the Julia setJ(f). The aim of this paper is to prove that the free energy can be represented as the logarithmic potential of the maximal entropy measure onJ(f). Moreover, using this representation, we can show a close relationship between the critical exponent and local similarity of this measure.
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allfields	(DE-627)NLEJ197937977 DE-627 ger DE-627 rakwb eng Ising models, julia sets, and similarity of the maximal entropy measures 1995 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this model is a rational endomorphism (denoted byf) of Ĉ and that the singularities of the free energy lie on the Julia setJ(f). The aim of this paper is to prove that the free energy can be represented as the logarithmic potential of the maximal entropy measure onJ(f). Moreover, using this representation, we can show a close relationship between the critical exponent and local similarity of this measure. Springer Online Journal Archives 1860-2002 Ishii, Yutaka oth in Journal of statistical physics 1969 78(1995) vom: März/Apr., Seite 815-825 (DE-627)NLEJ188991786 (DE-600)2017302-7 1572-9613 nnns volume:78 year:1995 month:03/04 pages:815-825 extent:11 http://dx.doi.org/10.1007/BF02183689 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 78 1995 3/4 815-825 11
spelling	(DE-627)NLEJ197937977 DE-627 ger DE-627 rakwb eng Ising models, julia sets, and similarity of the maximal entropy measures 1995 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this model is a rational endomorphism (denoted byf) of Ĉ and that the singularities of the free energy lie on the Julia setJ(f). The aim of this paper is to prove that the free energy can be represented as the logarithmic potential of the maximal entropy measure onJ(f). Moreover, using this representation, we can show a close relationship between the critical exponent and local similarity of this measure. Springer Online Journal Archives 1860-2002 Ishii, Yutaka oth in Journal of statistical physics 1969 78(1995) vom: März/Apr., Seite 815-825 (DE-627)NLEJ188991786 (DE-600)2017302-7 1572-9613 nnns volume:78 year:1995 month:03/04 pages:815-825 extent:11 http://dx.doi.org/10.1007/BF02183689 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 78 1995 3/4 815-825 11
allfields_unstemmed	(DE-627)NLEJ197937977 DE-627 ger DE-627 rakwb eng Ising models, julia sets, and similarity of the maximal entropy measures 1995 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this model is a rational endomorphism (denoted byf) of Ĉ and that the singularities of the free energy lie on the Julia setJ(f). The aim of this paper is to prove that the free energy can be represented as the logarithmic potential of the maximal entropy measure onJ(f). Moreover, using this representation, we can show a close relationship between the critical exponent and local similarity of this measure. Springer Online Journal Archives 1860-2002 Ishii, Yutaka oth in Journal of statistical physics 1969 78(1995) vom: März/Apr., Seite 815-825 (DE-627)NLEJ188991786 (DE-600)2017302-7 1572-9613 nnns volume:78 year:1995 month:03/04 pages:815-825 extent:11 http://dx.doi.org/10.1007/BF02183689 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 78 1995 3/4 815-825 11
allfieldsGer	(DE-627)NLEJ197937977 DE-627 ger DE-627 rakwb eng Ising models, julia sets, and similarity of the maximal entropy measures 1995 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this model is a rational endomorphism (denoted byf) of Ĉ and that the singularities of the free energy lie on the Julia setJ(f). The aim of this paper is to prove that the free energy can be represented as the logarithmic potential of the maximal entropy measure onJ(f). Moreover, using this representation, we can show a close relationship between the critical exponent and local similarity of this measure. Springer Online Journal Archives 1860-2002 Ishii, Yutaka oth in Journal of statistical physics 1969 78(1995) vom: März/Apr., Seite 815-825 (DE-627)NLEJ188991786 (DE-600)2017302-7 1572-9613 nnns volume:78 year:1995 month:03/04 pages:815-825 extent:11 http://dx.doi.org/10.1007/BF02183689 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 78 1995 3/4 815-825 11
allfieldsSound	(DE-627)NLEJ197937977 DE-627 ger DE-627 rakwb eng Ising models, julia sets, and similarity of the maximal entropy measures 1995 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this model is a rational endomorphism (denoted byf) of Ĉ and that the singularities of the free energy lie on the Julia setJ(f). The aim of this paper is to prove that the free energy can be represented as the logarithmic potential of the maximal entropy measure onJ(f). Moreover, using this representation, we can show a close relationship between the critical exponent and local similarity of this measure. Springer Online Journal Archives 1860-2002 Ishii, Yutaka oth in Journal of statistical physics 1969 78(1995) vom: März/Apr., Seite 815-825 (DE-627)NLEJ188991786 (DE-600)2017302-7 1572-9613 nnns volume:78 year:1995 month:03/04 pages:815-825 extent:11 http://dx.doi.org/10.1007/BF02183689 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 78 1995 3/4 815-825 11
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abstract	Abstract We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this model is a rational endomorphism (denoted byf) of Ĉ and that the singularities of the free energy lie on the Julia setJ(f). The aim of this paper is to prove that the free energy can be represented as the logarithmic potential of the maximal entropy measure onJ(f). Moreover, using this representation, we can show a close relationship between the critical exponent and local similarity of this measure.
abstractGer	Abstract We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this model is a rational endomorphism (denoted byf) of Ĉ and that the singularities of the free energy lie on the Julia setJ(f). The aim of this paper is to prove that the free energy can be represented as the logarithmic potential of the maximal entropy measure onJ(f). Moreover, using this representation, we can show a close relationship between the critical exponent and local similarity of this measure.
abstract_unstemmed	Abstract We study the phase transition of Ising models on diamondlike hierarchical lattices. Following an idea of Lee and Yang, one can make an analytic continuation of free energy of this model to the complex temperature plane. It is known that the Migdal-Kadanoff renormalization group of this model is a rational endomorphism (denoted byf) of Ĉ and that the singularities of the free energy lie on the Julia setJ(f). The aim of this paper is to prove that the free energy can be represented as the logarithmic potential of the maximal entropy measure onJ(f). Moreover, using this representation, we can show a close relationship between the critical exponent and local similarity of this measure.
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