Acta Mathematica

, Volume 211, Issue 2, pp 191–225 | Cite as

The energy density in the planar Ising model

  • Clément Hongler
  • Stanislav Smirnov


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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Copyright information

© Institut Mittag-Leffler 2013

Authors and Affiliations

  1. 1.Department of MathematicsColumbia UniversityNew YorkU.S.A.
  2. 2.Section de MathématiquesUniversité de GenèveGenève 4Switzerland
  3. 3.Chebyshev LaboratorySt. Petersburg State UniversitySt. PetersburgRussia

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