  We introduce a fast spatial point pattern analysis technique which is
suitable for systems of many identical particles giving rise to multi-particle
correlations up to arbitrary order. The obtained correlation parameters allow
to quantify the quality of mean field assumptions or theories that incorporate
correlations of limited order. We study the Vicsek model of self-propelled
particles and create a correlation map marking the required correlation order
for each point in phase space incorporating up to ten-particle correlations. We
find that multi-particle correlations are important even in a large part of the
disordered phase. Furthermore, the two-particle correlation parameter serves as
an excellent order parameter to locate both phase transitions of the system,
whereas two different order parameters were required before.
