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

physical review. e

Multiparameter universality and directional nonuniversality of exact  anisotropic critical correlation functions of the two-dimensional Ising  universality class