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Description
The existence of the inhomogeneous chiral phase, where the chiral condensate is spatially modulated has been discussed from some effective model analysis.
The phase seems to emerge in compact stars because it appears around the conventional chiral phase transition line in the QCD phase diagram.
Assuming an inhomogeneous configuration called "dual chiral density wave (DCDW)", where both scalar and pseudoscalar condensates are spatially modulated,
the external magnetic field extends the DCDW phase over the low chemical potential ($\mu$) region except for $\mu=0$ in the chiral limit [1].
It seems the spread DCDW phase can be explored by the lattice QCD simulation.
Therefore we constitute the thermodynamic potential including the finite current quark mass around the critical point by the generalized Ginzburg-Landau expansion [2] to consider the effect of the explicit chiral symmetry breaking on the inhomogeneous chiral phase transition.
Consequently, we can see that the strong magnetic field extends the DCDW phase over the low $\mu$ region even if the current quark mass is finite [3].
The possibility of the exploration by the lattice QCD is phenomenologically discussed based on the result.
Besides, the inverse magnetic catalysis is also argued in the present model.
Reference
[1] T. Tatsumi, K. Nishiyama and S. Karasawa, Phys. Lett. B743, 66 (2015)
[2] D. Nickel, Phys. Rev. Lett. 103, 072301 (2009)
[3] R. Yoshiike and T. Tatsumi, Phys. Rev. D92, 116009 (2015)
