  We investigate the stability of the Magnetic Dual Chiral Density Wave (MDCDW)
phase of cold and dense QCD against collective low-energy fluctuations of the
order parameter. The appearance of additional structures in the system
free-energy due to the explicit breaking of the rotational and isospin
symmetries by the external magnetic field and the field-induced asymmetry of
the lowest Landau level modes play a crucial role in the analysis. The new
structures not only affect the condensate minimum equations, but also the
spectrum of the thermal fluctuations, which lacks the transverse soft modes
that typically affect single-modulated inhomogeneous phases in the absence of a
magnetic field. Consequently, the long-range order of the MDCDW phase is
preserved at finite temperature. The lack of Landau-Peierls instabilities in
the MDCDW phase makes this inhomogeneous phase of dense quark matter
particularly relevant for the physics of neutron stars.
