  We prove the validity of multiparameter universality for the exact critical
bulk correlation functions of the anisotropic square-lattice and
triangular-lattice Ising models on the basis of the exact scaling structure of
the correlation function of the two-dimensional anisotropic scalar $\varphi^4$
model with four nonuniversal parameters. The correlation functions exhibit a
directional nonuniversality due to principal axes whose orientation depends on
microscopic details. In particular we determine the exact anisotropy matrices
governing the bulk and finite-size critical behavior of the $\varphi^4$ and
Ising models. We also prove the validity of multiparameter universality for an
exact critical bulk amplitude relation.
