11th Bologna Workshop on Conformal Field Theory and Integrable Models

Tracy-Widom distribution in the six-vertex model

4 Sept 2025, 10:05

25m

Aula Magna (Dept. of Physics and Astronomy - University of Bologna)

Talk (25 min) Talks

Speaker

Filippo Colomo (Istituto Nazionale di Fisica Nucleare)

Description

We consider the six-vertex model on the N x N lattice, with domain
wall boundary conditions, and at ice-point, $\Delta=1/2$. We focus on
the Emptiness Formation Probability (EFP), for which we build an
explicit and exact (although still conjectural) expression, as the
Fredholm determinant of some linear integral operator. We study the
asymptotic behaviour of the obtained representation at large N. In
particular, by tuning the geometric parameters of the EFP to the
vicinity of the arctic curve, we obtain the GUE Tracy-Widom
distribution. Joint work with Andrei Pronko. [Nucl. Phys. B 1004 (2024) 116565]

Presentation materials

bologna.pdf