GAMP seminar by A. Glazman (Tel Aviv U)
GAMP (Geometric Analysis and Mathematical Physics) Seminar
Speaker: Alexander Glazman (Tel Aviv U).
Title: Probabilistic approach to phase transitions in lattice models.
Abstract: Phase transitions are natural phenomena in which a small change in an external parameter causes a dramatic change in the qualitative structure of the object (e.g. iron loses its ferromagnetic properties above a critical temperature). To analyse these transitions, scientists proposed the abstract framework of lattice models: the material is modeled as a collection of particles on a regular lattice, interacting only with their nearest neighbours.
An essential tool in the mathematical study of these models is the positive correlation (FKG) inequality. In the particular case of a uniformly chosen Lipschitz function on the triangular lattice, we show new FKG properties and use them to prove that the model exhibits logarithmic fluctuations. This provides the first rigorous evidence for the conjecture that the scaling limit of the surface is the Gaussian Free Field. (This is joint work with Ioan Manolescu).