Infrared behaviour of massless integrable flows entering the minimal models from φ31

It is known that any minimal model Mp receives along its φ31 irrelevant direction two massless integrable flows: one from Mp+1 perturbed by φ13, the other from Zp−1 parafermionic model perturbed by its generating parafermion field. By comparing Thermodynamic Bethe Ansatz data and “predictions” of infrared Conformal Perturbation Theory we show that these two flows are received by Mp with opposite coupling constants of the φ31 irrelevant perturbation. Some comments on the massless S-matrices of these two flows are added.