Delocalisation of the long-range Gaussian chain

26.05.2025 16:15 – 18:00

Abstract:
I will speak about the localisation/delocalisation properties of the discrete Gaussian chain with long-range interactions, which was the object of several conjectures since the nineties.
In a first paper with van Enter, Le Ny and Ruszel, we cooked up a very short proof of the absence of shift-invariant Gibbs states at any temperature for any interaction decay power α>2, which shows delocalisation of the chain in a non-quantitative manner.
Later on, in a second paper with Dario and Le Ny, we obtained a quantitative version of this delocalisation.
Combined with the results of Kjaer-Hilhorst, Fröhlich-Zegarlinski and Garban, our estimates provide an (almost) complete picture for the localisation/delocalisation of the discrete Gaussian chain. The proofs are based on graph surgery techniques which have been recently developed by van Engelenburg-Lis and Aizenman-Harel-Peled-Shapiro to study the phase transitions of two dimensional integer-valued height functions (and of their dual spin systems).

Lieu

Bâtiment: Conseil Général 7-9

Conseil Général 7-9, Room 1-15, Séminaire Math Physics

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