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In planar lattice statistical mechanics models like coupled Ising withquartic interactions, vertex and dimer models, the exponents depend on all theHamiltonian details. This corresponds, in the Renormalization Group language,to a line of fixed points. A form of universality is expected to hold, implyingthat all the exponents can be expressed by exact "Kadanoff" relations in termsof a single one of them. This conjecture has been recently established and wereview here the key step of the proof, obtained by rigorous RenormalizationGroup methods and valid irrespectively on the solvability of the model. Theexponents are expressed by convergent series in the coupling and, thanks to aset of cancellations due to emerging chiral symmetries, the extended scalingrelations are proven to be true.

Universality for critical lines for Ising, Vertex and Dimer models