The energy density in the planar Ising model

Clément Hongler Department of Mathematics, Columbia University Stanislav Smirnov Section de Mathématiques, Université de Genève

Dynamical Systems Probability mathscidoc:1701.11005

Acta Mathematica, 211, (2), 191-225, 2011.7
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
[ Download ] [ 2017-01-08 20:34:01 uploaded by actaadmin ] [ 175 downloads ] [ 0 comments ] [ Cited by 21 ]
  title={The energy density in the planar Ising model},
  author={Clément Hongler, and Stanislav Smirnov},
  booktitle={Acta Mathematica},
Clément Hongler, and Stanislav Smirnov. The energy density in the planar Ising model. 2011. Vol. 211. In Acta Mathematica. pp.191-225.
Please log in for comment!
Contact us: | Copyright Reserved