Citation histories of papers: sometimes the rich get richer, sometimes they don't

We describe a simple model of how a publication's citations change over time, based on pure-birth stochastic processes with a linear cumulative advantage effect. The model is applied to citation data from the Physical Review corpus provided by APS. Our model reveals that papers fall into three different clusters: papers that have rapid initial citations and ultimately high impact (fast-hi), fast to rise but quick to plateau (fast-flat), or late bloomers (slow-late), which may either never achieve many citations, or do so many years after publication. In "fast-hi" and "slow-late", there is a rich-get-richer effect: papers that have many citations accumulate additional citations more rapidly while the "fast-flat" papers do not display this effect. We conclude by showing that only a few years of post-publication statistics are needed to identify high impact ("fast-hi") papers.