論文

査読有り
1995年7月

2-NEIGHBOR STOCHASTIC CELLULAR-AUTOMATA AND THEIR PLANAR LATTICE DUALS

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
  • M KATORI
  • ,
  • H TSUKAHARA

28
14
開始ページ
3935
終了ページ
3957
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1088/0305-4470/28/14/014
出版者・発行元
IOP PUBLISHING LTD

Two-neighbour stochastic cellular automata (SCA) are the set of one-dimensional discrete-time interacting particle systems with two parameters, which show non-equilibrium phase transitions from the extinction phase to the survival phase. The phase diagram was first studied by Kinzel using a numerical method called transfer-matrix scaling. For some parameter region the processes can be defined as directed percolation models on the spatio-temporal plane and the bond- and site-directed percolation models are included as special cases. Extending the argument of Dhar, Barma and Phani originally given for bond-directed percolation, we introduce diode-resistor percolation models which are the planar lattice duals of the SCA and give rigorous lower bounds for the critical line. In special cases, our results give 0.6885 less than or equal to alpha(c) and 0.6261 less than or equal to beta(c), where alpha(c) and beta(c) denote the critical probabilities of the site- and bond-directed percolation models on the square lattice. respectively. Combining the upper bound for the critical line recently proved by Liggett, we summarize the rigorous results for the phase diagram of the systems. Results of computer simulation are also shown.

リンク情報
DOI
https://doi.org/10.1088/0305-4470/28/14/014
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:A1995RM21300014&DestApp=WOS_CPL
ID情報
  • DOI : 10.1088/0305-4470/28/14/014
  • ISSN : 0305-4470
  • Web of Science ID : WOS:A1995RM21300014

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