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

Volker Dohm
Author Information
  1. Volker Dohm: Institute for Theoretical Physics, RWTH Aachen University, D-52056 Aachen, Germany.

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 φ^{4} model with four nonuniversal parameters. The correlation functions exhibit a directional nonuniversality due to principal axes whose orientation depends on microscopic details. We determine the exact anisotropy matrices governing the bulk and finite-size critical behavior of the φ^{4} and Ising models. We also prove the validity of multiparameter universality for an exact critical bulk amplitude relation.

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