This <a href="http://en.wikipedia.org/wiki/Cluster_expansion"><i>stat-phys thing</i> (cluster expansion)</a> and that <a href="http://en.wikipedia.org/wiki/Cluster_decomposition_theorem"><i>qft thing</i> (cluster decomposition)</a> are related by both referring to the notion of <a href="http://en.wikipedia.org/wiki/Cluster">cluster, being "<i>a small group or bunch of something.</i>"</a>;     

 - the former referring rather to cluster in the sense of a "<i>group</i>" of some particular (small, or large) **number** of members,    
with particular and primary attention given to **pairwise** membership (thus not including clusters in the degenerate sense of having only one member),
   
 - the latter referring rather to cluster in the sense of a "<i>bunch</i>" of members that are **coincident**,    
thereby characterizing pairs of members of distinct bunches as **not** coincident (and including the notion of a bunch in the degenerate sense of having only one member).

(More might be said, 'cause that's really my kinda bag ...)