Acta Mathematica

The energy density in the planar Ising model

Clément Hongler and Stanislav Smirnov

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Abstract

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.

Article information

Source
Acta Math., Volume 211, Number 2 (2013), 191-225.

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

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485892736

Digital Object Identifier
doi:10.1007/s11511-013-0102-1

Mathematical Reviews number (MathSciNet)
MR3143889

Zentralblatt MATH identifier
1287.82007

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

Rights
2013 © Institut Mittag-Leffler

Citation

Hongler, Clément; Smirnov, Stanislav. The energy density in the planar Ising model. Acta Math. 211 (2013), no. 2, 191--225. doi:10.1007/s11511-013-0102-1. https://projecteuclid.org/euclid.acta/1485892736


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