On Duality Between Continuous Spin Models and Height Functions

by Diederik van Engelenburg (University of Lyon 1)

Friday May 24, 2024, 2:00 PM → 4:00 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Probability and analysis informal seminar

Classical spin models taking value in the circle are naturally dual to spin models taking value in the integers (on the dual graph). Unlike in the context of Ising/Potts models, this duality is only visible at the level of order-disorder operators, there are no bijections between the models (as far as we know). I will revisit these well known relations, and will argue how the continuous symmetry group of S^1 will help to prove different results for the spin model and dual height function model. Notably, I will show a type of Gaussian domination holds for the height function on any graph, I will mention how it can be used to prove the Berezinskii--Kosterlitz--Thouless transition and time permitting, I will present some other results. All is based on joint work with Marcin Lis. 
 

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