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Height function delocalisation on cubic planar graphs

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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 XY and Villain models on the triangular lattice.

This talk is part of the Probability series.

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