【摘要】 <正> 设S是一可数的位置集,S的每个位置上有一个实体(如一个粒子),它有正的或负的自旋,分别记为1和0。X={0,1}~s表示系统的自旋的一切组态。以X为相空间的Markov过程描述自旋组态的演化,在[1]中讨论了一类这样的过程——自旋变相过程——的存在及唯一性和可逆测度等问题。本文中,我们引进速度函数的拟可逆测度概念,用[3]中的场论思想讨论紧邻速度函数的拟可逆测度。在§2中,我们证明紧邻速度函数的拟可逆测度是Markov随机场,并给出拟可逆测度存在的充分必要条件;§3中给出拟更多还原

【Abstract】 Let S be a countable set with a graph structure. The process with state space X={0,1}~s is described in terms of a collection of nonnegative speed functions c(u,·), u∈S. In this paper, we introduce the concept of quasi-reversible measure for speed functions, and discuss some properties contained in the existence and uniqueness of quasi-reversible measures for the nearest neighbour speed functions, with the idea of field theory by Hou and Chen. In section 2, we show that quasi-reversible measures are Markov random fields. A necessary and sufficient condition for the existence of quasi-reversible measures is presented. In section 3, a uniqueness theorem of quasi-reversible measures is given. The problem to determine the quasi-reversible measures in accordance with the speed function is discussed, for some particular cases, the quasi-reversible measures can be computed explicitly. In section 4, we show that if the speed functions are uniformly bounded, and each point of S has uniformly bounded boundary, then the uasi-reversible measures of the speed functions are reversible measures of the spin-flip process with the speed functions. Thus we obtain the necessary and sufficient conditions for the existence and uniqueness of reversible measures for spin-flip process with nearest neighbour speed functions. Particularly if speed functions are defined by the nearest neighbour potential, then quasi-reversible measures exist, thus our results can be applied to solve the uniqueness problem of Gibbs states with the nearest neighbour potential.更多还原