  In planar lattice statistical mechanics models like coupled Ising with
quartic interactions, vertex and dimer models, the exponents depend on all the
Hamiltonian details. This corresponds, in the Renormalization Group language,
to a line of fixed points. A form of universality is expected to hold, implying
that all the exponents can be expressed by exact "Kadanoff" relations in terms
of a single one of them. This conjecture has been recently established and we
review here the key step of the proof, obtained by rigorous Renormalization
Group methods and valid irrespectively on the solvability of the model. The
exponents are expressed by convergent series in the coupling and, thanks to a
set of cancellations due to emerging chiral symmetries, the extended scaling
relations are proven to be true.
