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.


Published in:
Acta Math., 211, 191-225
Year:
2013
Laboratories:




 Record created 2014-07-18, last modified 2018-03-17

n/a:
Download fulltext
PDF

Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)