中国物理B ›› 2002, Vol. 11 ›› Issue (8): 771-775.doi: 10.1088/1009-1963/11/8/304

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A mean-field approximation scheme containing the spatial parameter and its application to a surface-reaction-like cellular automaton model

张震1, 余仲秋2, 张波涛2   

  1. (1)Electrical Engineering Institute, Zhengzhou University, Zhengzhou 450002, China; (2)Physics Group, Information Engineering University, Zhengzhou 450002, China
  • 收稿日期:2002-01-20 修回日期:2002-04-23 出版日期:2002-08-12 发布日期:2005-06-12

A mean-field approximation scheme containing the spatial parameter and its application to a surface-reaction-like cellular automaton model

Yu Zhong-Qiu (余仲秋)a, Zhang Zhen (张震)b, Zhang Bo-Tao (张波涛)a   

  1. a Physics Group, Information Engineering University, Zhengzhou 450002, China; b Electrical Engineering Institute, Zhengzhou University, Zhengzhou 450002, China
  • Received:2002-01-20 Revised:2002-04-23 Online:2002-08-12 Published:2005-06-12

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摘要： Using an AB2 surface-reaction-like cellular automaton model, we present a modified mean-field approximation scheme for describing some dynamic lattice models, in which a lattice freedom parameter N is introduced as a variable. We obtain the phase diagrams of the example model for linear, hexagonal, square and triangular lattices, and we reveal a second-order phase transition which has not been found using traditional approaches.

Abstract: Using an AB2 surface-reaction-like cellular automaton model, we present a modified mean-field approximation scheme for describing some dynamic lattice models, in which a lattice freedom parameter N is introduced as a variable. We obtain the phase diagrams of the example model for linear, hexagonal, square and triangular lattices, and we reveal a second-order phase transition which has not been found using traditional approaches.

Key words: mean-field scheme, dynamic lattice model, phase transition

中图分类号:  (Lattice theory and statistics)

  • 05.50.+q
05.70.Fh (Phase transitions: general studies) 05.20.Dd (Kinetic theory)