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Using analogies between flow equations from the Functional RenormalizationGroup and flow equations from (numerical) fluid dynamics we investigate theeffects of bosonic fluctuations in a bosonized Gross-Neveu model -- namely theGross-Neveu-Yukawa model. We study this model for finite numbers of fermions atvarying chemical potential and temperature in the local potentialapproximation. Thereby we numerically demonstrate that for any finite number offermions and as long as the temperature is non-zero, there is no $\mathbb{Z}_2$symmetry breaking for arbitrary chemical potentials.

Bosonic fluctuations in the $( 1 + 1 )$-dimensional Gross-Neveu(-Yukawa) model at varying $\mu$ and $T$ and finite $N$