Conformal Geometry Program Lecture Series: Dmitry Chelkak, Steklov Institute

Dmitry Chelkak (Steklov Institute (PDMI RAS) & Chebyshev Lab, St.Petersburg)

Title: Spin Correlations in the Planar Ising Model via Fermionic Observables. Part II.
Speaker: Dmitry Chelkak (Steklov Institute (PDMI RAS) & Chebyshev Lab, St.Petersburg)
Date: Wednesday, March 6, 2013
Time: 4:00pm – 5:30pm
Place: Seminar Room 313, Simons Center




Abstract: Based on recent joint projects with Clement Hongler and Konstantin Izyurov. The main goal of the minicourse is to discuss the rigorous proof of existence and conformal covariance of scaling limits of spin correlations in the critical Ising model in bounded planar domains.

We discuss the spin-spin expectations in the critical Ising model defined on refining square grid approximations of a given planar domain. The main idea is to extract the information about spin-spin expectations considering the limit of discrete holomorphic observables and the continuous counterpart of the boundary value problem which they solve in a discrete setup. This approach works, at least for some boundary conditions, for any (not necessary simply connected) planar domain, in particular, providing a new explanation of the famous 1/8 scaling exponent as the simple conformal covariance property of that boundary value problem.