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 correlator and compute its scaling limit by discrete complex analysis methods. As a consequence, we obtai...

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Veröffentlicht in:Acta mathematica 2013-12, Vol.211 (2), p.191-225
Hauptverfasser: Hongler, Clément, Smirnov, Stanislav
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0001-5962
1871-2509
DOI:10.1007/s11511-013-0102-1