数学物理学报(英文版) ›› 1986, Vol. 6 ›› Issue (2): 213-222.

• 论文 • 上一篇    下一篇

THE SET OF THE INVARIANT MEASURES OF BOUNDED SPIN-FLIP PROCESSES WITH POTENTIAL

唐守正   

  1. Department of Mathematics, Beijing Normal University, Beijing, China
  • 收稿日期:1984-06-11 出版日期:1986-06-25 发布日期:1986-06-25

THE SET OF THE INVARIANT MEASURES OF BOUNDED SPIN-FLIP PROCESSES WITH POTENTIAL

Tang Shouzheng   

  1. Department of Mathematics, Beijing Normal University, Beijing, China
  • Received:1984-06-11 Online:1986-06-25 Published:1986-06-25

摘要: In this paper, some properties of the invariant measures of bounded spin-flip processes are discussed. It is proved that all invariant measures of a bounded spinflip process with potential are reversible measures if its speed functions have locally finite range interaction. Therefore, all invariant measures of the process are the Gibbs states of the potential. It is also proved that for each given potential, there exists a spin-flip process suth that all of its invariant measures are the Gibbs states of the potential.

Abstract: In this paper, some properties of the invariant measures of bounded spin-flip processes are discussed. It is proved that all invariant measures of a bounded spinflip process with potential are reversible measures if its speed functions have locally finite range interaction. Therefore, all invariant measures of the process are the Gibbs states of the potential. It is also proved that for each given potential, there exists a spin-flip process suth that all of its invariant measures are the Gibbs states of the potential.