at instances to sizeable and unforeseen effects. Of particular importance for the present work is that the strength of the $8q$ coupling is strongly correlated with the temperature and slope at which the crossover occurs and that it can be regulated together with the four-quark coupling, leaving the meson spectra at $T=0$ unaffected (with exception of the scalar $\sigma$ meson mass which decreases with increasing $8q$ coupling) [@Osipov:2008]. As a result the symmetry breaking for large $8q$ couplings is induced by the $6q$ ’t Hooft coupling strength, as opposed to the case with small $8q$ coupling, where the dynamical breaking of symmetry is controlled by the $4q$ coupling strength [@Osipov:2006a]. We would like to comment on a natural question which arises here, namely, can higher order many-quark interactions be also important? With regard to this, explicit argumets of A. A. Andrianov and V. A. Andrianov are known [@Andrianov:1993], which show that the structure of the QCD-motivated models at low energies with effective multi-fermion interactions and a finite cut-off in the chiral symmetry-breaking regime should contain only the vertices with four, six and eight-fermion interactions in four dimensions. This result explains partly the approximation used in our work.

Thus, in this 