The boundary spin correlations for planar Ising models have a well-known Pfaffian structure. For Ising models on the square lattice with finite-range interactions, the corresponding graph is not planar and the Pfaffian structure no long holds. Nevertheless, at criticality, the Pfaffian structure of boundary correlations emerges asymptotically (when boundary points are taken far apart). The proven statement establishes an aspect of universality in two dimensions beyond the solvable cases. In this talk, I will present this result and discuss the main ideas of proof, that involve a percolation interpretation of the problem (via Aizenman random currents, and FK percolation) and recent progress in percolation theory (robust Russo-Seymour-Welsh theory). This talk is based on a joint work with Michael Aizenman, Hugo Duminil-Copin and Simone Warzel.
By Wendelin Werner
By Victor Dotsenko
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By Rafael Greenblatt
By Eveliina Peltola
By Giuseppe Mussardo
By Yvan Velenik
By Michele Caselle
By Ara Sedrakyan
By Michael Aizenman
By Jürg Fröhlich , Tom Spencer , Arthur Jaffe , Geoffrey Grimmett , Joel Lebowitz
By Vincent Tassion
By Clément Delcamp
By Claudio Dappiaggi
By Alexander Strohmaier
By Hans Lindblad
By Misha Gromov
By Olivier Benoist
By Viviane Pons
By Viviane Pons
