  We use both mean-field methods and numerical simulation to study the phase
diagram of classical particles interacting with a hard-core and repulsive, soft
shoulder. Despite the purely repulsive interaction, this system displays a
remarkable array of aggregate phases arising from the competition between the
hard-core and shoulder length scales. In the limit of large shoulder width to
core size, we argue that this phase diagram has a number of universal features,
and classify the set of repulsive shoulders that lead to aggregation at high
density. Surprisingly, the phase sequence and aggregate size adjusts so as to
keep almost constant inter-aggregate separation.

Soft Condensed Matter;Statistical Mechanics