  The characteristics of the $h$-index in the field of condensed matter physics
are studied using high-quality data from ResearcherID. The results are examined
in terms of theoretical descriptions of the $h$-index' overall dependence on a
researcher's total number of published papers, and total number of citations.
In particular, the models by Hirsch, Egghe and Rousseau, as well as by
Gl\"anzel and Schubert are examined. Special emphasis is placed on the
deviations from such statistical descriptions, and it is argued that the
deviation of a particular researcher's $h$ value from the Egghe-Rouseau model's
prediction can be used as a supplementary measure of impact. A corresponding
analysis with similar results is performed using the multi-author $h_m$-index.
