Based on the premise that a cluster expansion is defined by the clusters that it includes, and that once a set of clusters is selected for a cluster expansion it gives a specific value for the configurational energy of any particular structure, a proof for invariance of cluster expansions is presented. A cluster expansion is invariant under linear transformations of the site occupation variable when it includes all the subclusters of the included clusters. When the spin- or site-occupation variable is redefined, the consequence for an invariant cluster expansion is that the numerical values of the effective cluster interactions change, without there being any other changes. Therefore, the spin- or site-occupation variable can be defined at will, say, to optimize computational expediency.
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|Publication status||Published - 2005 Jun 1|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics