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Extending the results obtained in the case $N$ odd, the effect of slightlyrelevant perturbations of the second parafermionic field theory with thesymmetry $\mathbb{Z}_{N}$, for $N$ even, are studied. The renormalization groupequations, and their infra red fixed points exhibit the same structure in bothcases. In addition to the standard flow from the $p$-th to the $(p-2)$-thmodel, another fixed point corresponding to the $(p-1)$-th model is found.

Renormalization group flows for the second $\mathbb{Z}_{N}$ parafermionic field theory for $N$ even