Dimer problem in statistical mechanics-an exact result
Dimer problem in statistical mechanics-an exact result
复制标题
DOI：
10.1080/14786436108243366
复制
发表时间：
1961-08
影响因子：
1.6
通讯作者：
H. Temperley;M. Fisher
中科院分区：
文献类型：
--
作者：
H. Temperley;M. Fisher
摘要包含双原子分子的体系(例如溶液或气体)的一个重要的、尽管在物理上过于简化的模型是由“刚性二聚体”占据的晶格模型(例如，Fowler和Rushbrook1937)。每个二聚体填充晶格上最近的两个位置，任何位置都不能被一个以上的二聚体占据。这代表了一个具有一定难度的统计学问题，到目前为止只在一个维度上得到了精确的解决(Green和Leipnik 1960年，Fisher和Temperley 1960年)。(不同的作者已经在近似统计方法的基础上进行了处理，例如Rushbrooke等。(1953)本文给出了平面正方形晶格上二聚体问题的一个精确解，即当二聚体完全填满晶格时(密排或高密度极限)。
Abstract An important, even though physically oversimplified model of a system (e.g. solution or gas) containing diatomic molecules is that of a lattice occupied by ‘rigid dimers’ (e.g. Fowler and Rushbrooke 1937). Each dimer fills two nearest-neighbour sites on the lattice and no site may be occupied by more than one dimer. This represents a statistical problem of some difficulty which has so far been solved exactly only in one dimension (Green and Leipnik 1960, Fisher and Temperley 1960). (It has been treated by various authors on the basis of approximate statistical methods, e.g. Rushbrooke et al. (1953).) This note reports an exact solution for the dimer problem on the plane square lattice in the limiting case where the dimera completely fill the lattice (close-packed or high density limit).