  Colloidal particles self assemble into a wide range of structures under
external AC electric fields due to induced dipolar interactions [Yethiraj and
Van Blaaderen Nature 421 513 (2003)]. As a result of these dipolar
interactions, at low volume fraction the system is modulated between a
hard-sphere like state (in the case of zero applied field) and a "string fluid"
upon application of the field. Using both particle-resolved experiments and
Brownian dynamics simulations, we investigate the emergence of the string fluid
with a variety of structural measures including two-body and higher-order
correlations. The higher-order structure we probe using three-body spatial
correlation functions and a many-body approach based on minimum energy clusters
of a dipolar-Lennard-Jones system. This yields a series of geometrically
distinct minimum energy clusters upon increasing the strength of the dipolar
interaction, which are echoed in the higher-order structure of the colloidal
fluids we study here. We find good agreement between experiment and simulation
at the two-body level, although some discrepancies are found at higher field
strength, where the system falls out of equilibrium. Higher-order correlations
exhibit reasonable agreement between experiment and simulation, again with more
discrepancy at higher field strength for three--body correlation functions. At
higher field strength, the cluster population in our experiments and
simulations is dominated by the minimum energy clusters for all sizes $8 \leq m
\leq 12$. The agreement that we find here is notable considering that there is
no fit parameter in our mapping between experiment and simulation.
