Kashaev's relation for the Ising model, and a loop model

by Prof. Paul Melotti (LPSM)

Wednesday Nov 21, 2018, 4:30 PM → 5:30 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

In 1996 Rinat Kashaev introduced a new way to write the star-triangle move (or Yang-Baxter equations) of the Ising model as a single polynomial relation. In 2013 Richard Kenyon and Robin Pemantle understood that this relation could be seen as a kind of spatial recurrence. I will show how the iteration of Kashaev's recurrence can be related the combinatorics of a loop model with two colors, that was introduced for different reasons by Ole Warnaar and Bernard Nienhuis in 1993. It is also possible to couple this loop model with known relatives of the Ising model: a dimer model and a six-vertex model. Finally I will show a few limit shape phenomena.