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 researchers total number of published papers, and total number of citations. In particular, the models by Hirsch, Egghe and Rousseau, as well as by Glanzel 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 researchers $h$ value from the Egghe-Rouseau models 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.
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