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

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 ${\phi }^4$ 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 ${\phi }^4$ and Ising models. We also prove the validity of multiparameter universality for an exact critical bulk amplitude relation.

6 pages, 2 figures

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• Crossover from low-temperature to high-temperature fluctuations. I. Thermodynamic Casimir forces of isotropic systems
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Cited by in corpus (4)

• Exact Critical Casimir Amplitude of Anisotropic Systems from Conformal Field Theory and Self-Similarity of Finite-Size Scaling Functions in $d\ge 2$ Dimensions
• Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems
• Multiparameter universality and conformal field theory for anisotropic confined systems: test by Monte Carlo simulations
• Anomalous scaling corrections and quantum phase diagram of the Heisenberg antiferromagnet on the spatially anisotropic honeycomb lattice