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Paper Abstract and Keywords
Presentation 2005-11-18 15:25
Ising Phase Transition Related to an Anomalous Structure of the Invariant Set in a Bernoulli Coupled Map Lattice -- A "Seed" of the Ising Transition hidden in the Invariant Set --
Kazumasa Takeuchi, Masaki Sano (Univ. of Tokyo)
Abstract (in Japanese) (See Japanese page) 
(in English) The thermodynamic formalism for dynamical systems with many degrees of freedom is extended to deal with time averages and fluctuations of some macroscopic quantity along typical orbits, and applied to a 1-dimensional Bernoulli coupled map lattice equivalent to the 1D Ising model. Thereby, it turns out that a seed of the Ising phase transition is embedded as an anomalous structure of the chaotic invariant set, which appears as a (1+1) dimensional q-phase transition, and the seed is hidden as a non-dominant term in the partition function. The Ising transition occurs when the anomalous part becomes a physically dominant one. This relation between the phase transition and the anomalous structure is demonstrated numerically, and is analytically shown for the low interaction limit where the partition function results in that of the 2-dimensional Ising model.
Keyword (in Japanese) (See Japanese page) 
(in English) phase transition / q-phase transition / Ising model / thermodynamic formalism / periodic orbit expansion / / /  
Reference Info. IEICE Tech. Rep., vol. 105, no. 416, NLP2005-67, pp. 31-36, Nov. 2005.
Paper # NLP2005-67 
Date of Issue 2005-11-11 (NLP) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
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Conference Information
Committee NLP  
Conference Date 2005-11-18 - 2005-11-19 
Place (in Japanese) (See Japanese page) 
Place (in English) Kyushu Institute of Technology 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Special session and general. Subject of special session is ``Randomness and prediction---from fundamentals to applications''. 
Paper Information
Registration To NLP 
Conference Code 2005-11-NLP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Ising Phase Transition Related to an Anomalous Structure of the Invariant Set in a Bernoulli Coupled Map Lattice 
Sub Title (in English) A "Seed" of the Ising Transition hidden in the Invariant Set 
Keyword(1) phase transition  
Keyword(2) q-phase transition  
Keyword(3) Ising model  
Keyword(4) thermodynamic formalism  
Keyword(5) periodic orbit expansion  
1st Author's Name Kazumasa Takeuchi  
1st Author's Affiliation The University of Tokyo (Univ. of Tokyo)
2nd Author's Name Masaki Sano  
2nd Author's Affiliation The University of Tokyo (Univ. of Tokyo)
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Date Time 2005-11-18 15:25:00 
Presentation Time 25 
Registration for NLP 
Paper # IEICE-NLP2005-67 
Volume (vol) IEICE-105 
Number (no) no.416 
Page pp.31-36 
#Pages IEICE-6 
Date of Issue IEICE-NLP-2005-11-11 

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