2D Ising model: correlation functions at criticality via Riemann-type boundary value problems

Abstract

In this note we overview recent convergence results for correlations in the critical planar nearest-neighbor Ising model. We start with a short discussion of the combinatorics of the model and a definition of fermionic and spinor observables. After that, we illustrate our approach to spin correlations by a derivation of two classical explicit formulae in the infinite-volume limit. Then we describe the convergence results (as the mesh size tends to zero, in arbitrary planar domains) for fermionic correlators, energy-density and spin expectations. Finally, we discuss scaling limits of mixed correlators involving spins, disorders and fermions, and the classical fusion rules for them.

20 pages, Proceedings of the 7ECM. Tiny changes in the notation/normalizations to keep the paper consistent with other texts