  A detailed numerical study of a recent proposal for exotic states of the
D3-probe D5 brane system with charge density and an external magnetic field is
presented. The state has a large number of coincident D5 branes blowing up to a
D7 brane in the presence of the worldvolume electric and magnetic fields which
are necessary to construct the holographic state. Numerical solutions have
shown that these states can compete with the the previously known chiral
symmetry breaking and maximally symmetric phases of the D3-D5 system. Moreover,
at integer filling fractions, they are incompressible with integer quantized
Hall conductivities. In the dual superconformal defect field theory, these
solutions correspond to states which break the chiral and global flavor
symmetries spontaneously. The region of the temperature-density plane where the
D7 brane has lower energy than the other known D5 brane solutions is
identified. A hypothesis for the structure of states with filling fraction and
Hall conductivity greater than one is made and tested by numerical computation.
A parallel with the quantum Hall ferromagnetism or magnetic catalysis
phenomenon which is observed in graphene is drawn. As well as demonstrating
that the phenomenon can exist in a strongly coupled system, this work makes a
number of predictions of symmetry breaking patterns and phase transitions for
such systems.
