The Energy Density in the Planar Ising Model

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 spinor 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.


Publié dans:
Acta Math., 211, 191-225
Année
2013
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 Notice créée le 2014-07-18, modifiée le 2019-03-16

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