  In the present work, we discuss the phase structure of bilayer and monolayer
phases in the (2+1)-dimensional defect field theory whose gravity dual is
obtained by embedding D5/anti-D5 probe flavour branes in the singular conifold.
We study in detail the embedding equations and compare the free energies of the
resulting configurations at non-zero temperature and external magnetic field
perpendicular to the defects. Moreover, we analyse the meson spectrum and
confirm the stability of the single bilayer solution.
