Speaker:
Hugo Duminil-Copin

Title:
Emergent planarity in 2D Ising models with finite-range interactions

Abstract:
The known Pfaffian structure of the boundary spin correlations, and more
generally order-disorder correlation functions, is given a new explanation
through simple topological considerations within the model's random current
representation. This perspective is then employed in the proof that the
Pfaffian structure of boundary spins emerges asymptotically at criticality
in Ising models on Z^2 with finite-range interactions. The analysis is
enabled by new results on the stochastic geometry of the corresponding
random currents. The proven statement establishes an aspect of
universality, seen here in the emergence of fermionic structures in two
dimensions beyond the solvable cases.