100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

Piet Lammers

Height function delocalisation on cubic planar graphs
Tuesday, 5 April, 2022 - 14:00 to 15:00
Résumé : 

Delocalisation plays an important role in statistical physics. This talk will discuss the delocalisation transition in the context of height functions, which are integer-valued functions on the square lattice or similar two-dimensional graphs. By drawing a link with a phase coexistence result for site percolation on planar graphs, we prove delocalisation for a broad class of height functions on planar graphs of degree three. The proof also uses a new technique for symmetry breaking. The analysis includes several popular models such as the discrete Gaussian model, the solid-on-solid model, and the uniformly random K-Lipschitz function. Inclusion of the first model also implies the BKT phase transition in the Villain model on the triangular lattice.


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