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In order to discuss the occurrence of a periodic condensate in the Euclidean3-dimensional ghost $O(1)$ model, a modified version of the effective averageaction (EAA) renormalization group (RG) method is developed, called by usFourier-Wetterich RG approach. It is proposed to start with an ansatz for theEAA, that contains terms, in addition to the usual ones, induced by the variousFourier-modes of the periodic condensate and to expand the EAA in functionalTaylor-series around the periodic background. The RG flow equations are derivedin the next-to-next-to-leading order of the gradient expansion (GE). Nofield-dependence of the derivative couplings have been taken into account and$Z_2$ symmetry of the EAA is preserved. Preliminary numerical results have beenobtained under various additional simplifying assumptions. The characteristicsof the Wilson-Fisher fixed point and the phase structure of the model have beendetermined numerically in the local potential approximation and in thenext-to-leading order of the GE, when the periodic condensate has been modelledby a single cosine mode in one spatial direction. From the preliminary resultsimportant information is gained on further possibilities to improve theproposed RG scheme.

Modified renormalization group method applied to the $O(1)$ ghost model with periodic condensate