  Using the AdS/CFT correspondence, we study the thermodynamic properties and
the phase diagram of matter fields on (2+1)-dimensional defects coupled to a
(3+1)-dimensional N=4 SYM "heat bath". Considering a background magnetic field,
(net) quark density, defect "magnitude" $\delta N_c$ and the mass of the
matter, we study the defect contribution to the thermodynamic potentials and
their first and second derivatives to map the phases and study their physical
properties.
  We find some features that are qualitatively similar to other systems e.g. in
(3+1) dimensions and a number of features that are particular to the defect
nature, such as its magnetic properties, unexpected properties at T->0 and
finite density; and the finite $\delta N_c$ effects, e.g. a diverging
susceptibility and vanishing density of states at small temperatures, a
physically consistent negative heat capacity and new types of consistent
phases.
