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

## TL;DR

This paper proves that the critical correlation functions of 2D anisotropic Ising models follow a multiparameter universality, with directional nonuniversality caused by principal axes depending on microscopic details, and determines the exact anisotropy matrices.

## Contribution

It establishes the validity of multiparameter universality for exact critical correlation functions and amplitude relations in anisotropic 2D Ising models, linking microscopic details to macroscopic critical behavior.

## Key findings

- Correlation functions exhibit directional nonuniversality due to principal axes.
- Exact anisotropy matrices are determined for bulk and finite-size behavior.
- Multiparameter universality is validated for amplitude relations.

## Abstract

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.