Statistics of clusters in binary linear lattices

Abstract

The statistics of clusters in binary linear lattices is studied on the assumption that the relative weight of an Al or Bm cluster is determined only by its size l or m, and is independent of the location of the cluster on the chain. The average cluster numbers and the variance of their fluctuations are calculated for two probability ensembles, the quasi-grand ensemble where the total number of units N varies, and the canonical ensemble where N is fixed. It is shown that in the latter case in the limit of large N the statistics of clusters is fully described by the cluster densities l and m, and a correlation function gAB(R) for which a susceptibility theorem is derived.