  It is shown that the inhomogeneous chiral condensate in the Gross-Neveu (GN)
model takes the chiral spiral form, even though the thermodynamic functional
depends only on the chiral scalar density. It is the inhomogeneity of the
chiral scalar condensate that drives the spatial modulations of the
pseudoscalar one. The result has broader implications once we start to think of
fundamental theories behind the effective models. In particular, some effective
interactions---which may be omitted for descriptions of the homogeneous
phases---can be dynamically enhanced due to the spatial modulations of the
large mean fields. Implications for the four-dimensional counterparts of the GN
model are discussed. In a quark matter context, proper forms of the effective
models for the inhomogeneous phases are speculated, through considerations on
the Fermi-Dirac sea coupling.
