  We study the well-known sociological phenomenon of gang aggregation and
territory formation through an interacting agent system defined on a lattice.
We introduce a two-gang Hamiltonian model where agents have red or blue
affiliation but are otherwise indistinguishable. In this model, all
interactions are indirect and occur only via graffiti markings, on-site as well
as on nearest neighbor locations. We also allow for gang proliferation and
graffiti suppression. Within the context of this model, we show that gang
clustering and territory formation may arise under specific parameter choices
and that a phase transition may occur between well-mixed, possibly dilute
configurations and well separated, clustered ones. Using methods from
statistical mechanics, we study the phase transition between these two
qualitatively different scenarios. In the mean-field rendition of this model,
we identify parameter regimes where the transition is first or second order. In
all cases, we have found that the transitions are a consequence solely of the
gang to graffiti couplings, implying that direct gang to gang interactions are
not strictly necessary for gang territory formation; in particular, graffiti
may be the sole driving force behind gang clustering. We further discuss
possible sociological -- as well as ecological -- ramifications of our results.
