  We study a holographic gauge theory dual to the D3/D5 intersection. We
consider a pure gauge B-field flux through the internal two-sphere wrapped by
the probe D5--brane, which corresponds to a non-commutative configuration of
adjoint scalars. There is a domain wall separating the theory into regions with
different ranks of the adjoint group. At zero temperature the theory is
supersymmetric and at finite temperature there is a critical point of a second
order phase transition. We study the corresponding critical exponents and find
that the second derivatives of the free energy, with respect to the bare mass
and the magnetic field, diverge with a critical exponent of -2/3.
