Web models as generalizations of statistical loop models.

Augustin Lafay

ENS

Mon, Nov. 29th 2021, 11:00

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

Two dimensional gases of non intersecting loops have been a subject of study in mathematical physics for more than thirty years because of their numerous connections to integrability, two dimensional conformal field theory, random geometry and combinatorics. In this talk, I will present a natural generalization of loop models to gases of graphs possessing branchings. These graphs are called webs and first appeared in the mathematical community as diagrammatic presentations of categories of representations of quantum groups. The web models posses properties similar to the loop models. For instance, it will be shown that they describe, for some tuning of the parameters, interfaces of spin clusters in Zn spin models. Focusing on the numerically more accesible case of Uq(sl3) webs (or Kuperberg webs), it is possible to identify critical phases that are analogous to the dense and dilute phases of the loop models. These phases are then described by a Coulomb Gas with a two component bosonic field.

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