The energy density in the planar Ising model

Clément Hongler Department of Mathematics, Columbia University Stanislav Smirnov Section de Mathématiques, Université de Genève

Dynamical Systems Probability mathscidoc:1701.11005

Acta Mathematica, 211, (2), 191-225, 2011.7
We study the critical Ising model on the square lattice in bounded simply connected domains with + and free boundary conditions. We relate the energy density of the model to a discrete fermionic correlator and compute its scaling limit by discrete complex analysis methods. As a consequence, we obtain a simple exact formula for the scaling limit of the energy field one-point function in terms of the hyperbolic metric. This confirms the predictions originating in physics, but also provides a higher precision.
Ising model; energy density; discrete analytic function; fermions; conformal invariance; hyperbolic geometry; conformal field theory
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@inproceedings{clément2011the,
  title={The energy density in the planar Ising model},
  author={Clément Hongler, and Stanislav Smirnov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203401617939778},
  booktitle={Acta Mathematica},
  volume={211},
  number={2},
  pages={191-225},
  year={2011},
}
Clément Hongler, and Stanislav Smirnov. The energy density in the planar Ising model. 2011. Vol. 211. In Acta Mathematica. pp.191-225. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203401617939778.
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