  We generalize the construction of connected branched polymers and the notion
of the volume of the space of connected branched polymers studied by Brydges
and Imbrie, and Kenyon and Winkler to any hyperplane arrangement A. The volume
of the resulting configuration space of connected branched polymers associated
to the hyperplane arrangement A is expressed through the value of the
characteristic polynomial of A at 0. We give a more general definition of the
space of branched polymers, where we do not require connectivity, and introduce
the notion of q-volume for it, which is expressed through the value of the
characteristic polynomial of A at -q. Finally, we relate the volume of the
space of branched polymers to broken circuits and show that the cohomology ring
of the space of branched polymers is isomorphic to the Orlik-Solomon algebra.
