On the duality between height functions and continuous spin systems.

Abstract: We revisit the well known duality relation between integer valued height functions and spin systems with O(2) symmetry.

We will apply some simple corollaries from this duality to transfer information from one model to the other.

First, we deduce a type of Gaussian domination for the height-function variance.

Second, we deduce the monotonicity of this variance with respect to a natural temperature parameter.

Finally, we show how “delocalisation” of planar height functions implies a so-called BKT phase transition in the dual (planar) spin models.

Posted on Mar 27, 2023 in Seminario de Probabilidades de Chile, Seminars