The six-vertex model on random graphs | Integrable System Lunch Seminar

Abstract

I will explain how to reformulate the 6v model on dynamical random lattices as an NxN matrixmodel. 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 eliptic theta functions. The scalinglimit where the size of the lattices diverge is achieved when the torus degenerates into an infinitecylinder. lt is argued that the scaling limit is described by a c=1 compactified boson coupled toLiouvile gravity. The situation is less clear for lattices with boundaries where the boundaryobservables computed in the matrix model show unusual behaviour and stil lack Liouville gravitydescription.

Speaker Intro

Ivan Kostov obtained his PhD in 1982 from the Moscow State University, with scientific advisersVladimir Feinberg and Alexander Migdal. Then he worked in the group of lvan Todorov at theINRNE Sofia, and since 1990 as a CNRS researcher at the IPhT, CEA-Saclay, France. Currently heis emeritus DR CNRS at lPhT and a visiting professor at UFES, Vitoria, Brazil.