  We present the first rigorous derivation of a number of universal relations
for a class of models with continuously varying indices (among which are
interacting planar Ising models, quantum spin chains and 1D Fermi systems), for
which an exact solution is not known, except in a few special cases. Most of
these formulas were conjectured by Luther and Peschel, Kadanoff, Haldane, but
only checked in the special solvable models; one of them, related to the
anisotropic Ashkin-Teller model, is novel.
