Tilted Solid on Solid is Liquid, at Least when Thawed

by Benoit Laslier (Paris Cité)

Friday Feb 14, 2025, 2:00 PM → 4:00 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Probability and analysis informal seminar

The Solid on Solid model is a mainstay of the modelisation of 2D interfaces in the physics literature and it has also received extensive attention in mathematics. In particular a major work of Frölich and Spencer showed that it exhibits a roughening transitions where at low temperature, the interface is extremely localized with O(1) fluctuations at the microscopic scale while at high temperature it delocalize with logarithmic variance.
However, almost all the existing literature focuses on the case where the interface is parallel to the main axis of the underlying lattice, as in a crystal facet, but of course this cannot be the case globally everywhere. We will show that, at least for a model with a small added potential, whenever the interface has a tilt the phenomenology changes completely : at low enough temperature prove that the behavior of the interface is rough (like the high temperature usual case) and provide a full scaling limit for the fluctuations. The main approach is a comparison to the zero-temperature case which can be described as lozenge tilings and a renormalization procedure to understand the asymptotic of an interacting tiling model.

  

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