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

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