Speaker: Sasha Glazman (University of Innsbruck)

Title: Six-vertex model in the FKG regime

Abstract:

The six-vertex model is in correspondence with graph homomorphisms from $Z^2$ to $Z$. If a face is a saddle, it receives weight $c$, otherwise, it receives weight $a$ or $b$. The distribution is proportional to the product of the weights. When $c \geq a, b$, a positive association (FKG) inequality provides additional tools.

We discuss two results:
$\bullet$ When $a, b \leq c \leq a+b$, we give a soft, purely probabilistic proof of delocalisation relying on the non-coexistence theorem of Zhang and Sheffield. The same argument also applies to random Lipschitz functions on the triangular lattice.
$\bullet$ When $c > a+b$ (localized regime), we show convergence of an interface under Dobrushin boundary conditions to the Brownian bridge.

Joint works with Dober, Lammers, Ott.

*Note change in time/date/location.