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 |
Download PDF |
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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 |
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thermodynamic formalism |
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periodic orbit expansion |
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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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Speaker |
Author-1 |
Date Time |
2005-11-18 15:25:00 |
Presentation Time |
25 minutes |
Registration for |
NLP |
Paper # |
NLP2005-67 |
Volume (vol) |
vol.105 |
Number (no) |
no.416 |
Page |
pp.31-36 |
#Pages |
6 |
Date of Issue |
2005-11-11 (NLP) |