Extended Scaling Relations for Planar Lattice Models

It is widely believed that the critical properties of several planar lattice systems, like the Eight Vertex or the Ashkin-Teller models, are well described by an effective continuum fermionic theory obtained as a formal scaling limit. On the basis of this assumption several extended scaling relations among their indices were conjectured. We prove the validity of some of them, among which the ones predicted by Kadanoff (Phys Rev Lett 39:903–905, 1977) and by Luther and Peschel (Phys Rev B 12:3908–3917, 1975).