The six-vertex model on random graphs
Organizers
Speaker
Ivan Kostov
Time
Monday, May 13, 2024 12:00 PM - 1:00 PM
Venue
A4-1
Abstract
I will explain how to reformulate the 6v model on dynamical random lattices as an NxN matrix model. The spectral curve of the 6v matrix model at large N is an infinite envelope of a two-dimensional torus. An explicit global parametrisation is found by elliptic theta functions. The scaling limit where the size of the lattices diverge is achieved when the torus degenerates into an infinite cylinder. It is argued that the scaling limit is described by a c=1 compactified boson coupled to Liouville gravity. The situation is less clear for lattices with boundaries where the boundary observables computed in the matrix model show unusual behaviour and still lack Liouville gravity description.
Speaker Intro
Ivan Kostov obtained his PhD in 1982 from the Moscow State University, with scientific advisers Vladimir Feinberg and Alexander Migdal. Then he worked in the group of Ivan Todorov at the INRNE Sofia, and since 1990 as a CNRS researcher at the IPhT, CEA-Saclay, France. Currently he is emeritus DR CNRS at IPhT and a visiting professor at UFES, Vitoria, Brazil.