  In order to discuss the occurrence of a periodic condensate in the Euclidean
3-dimensional ghost $O(1)$ model, a modified version of the effective average
action (EAA) renormalization group (RG) method is developed, called by us
Fourier-Wetterich RG approach. It is proposed to start with an ansatz for the
EAA, that contains terms, in addition to the usual ones, induced by the various
Fourier-modes of the periodic condensate and to expand the EAA in functional
Taylor-series around the periodic background. The RG flow equations are derived
in the next-to-next-to-leading order of the gradient expansion (GE). No
field-dependence of the derivative couplings have been taken into account and
$Z_2$ symmetry of the EAA is preserved. Preliminary numerical results have been
obtained under various additional simplifying assumptions. The characteristics
of the Wilson-Fisher fixed point and the phase structure of the model have been
determined numerically in the local potential approximation and in the
next-to-leading order of the GE, when the periodic condensate has been modelled
by a single cosine mode in one spatial direction. From the preliminary results
important information is gained on further possibilities to improve the
proposed RG scheme.
