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2013 The energy density in the planar Ising model
Clément Hongler, Stanislav Smirnov
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Acta Math. 211(2): 191-225 (2013). DOI: 10.1007/s11511-013-0102-1


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.


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Clément Hongler. Stanislav Smirnov. "The energy density in the planar Ising model." Acta Math. 211 (2) 191 - 225, 2013.


Received: 20 July 2011; Revised: 15 September 2012; Published: 2013
First available in Project Euclid: 31 January 2017

zbMATH: 1287.82007
MathSciNet: MR3143889
Digital Object Identifier: 10.1007/s11511-013-0102-1

Keywords: conformal field theory , conformal invariance , discrete analytic function , energy density , fermions , hyperbolic geometry , Ising model

Rights: 2013 © Institut Mittag-Leffler

Vol.211 • No. 2 • 2013
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