Scott Mason: Dimer-dimer correlations at the rough-smooth boundary

Abstract

From previous results on infinite planar dimer models in a fixed phase, we know that pairs of dimers separated by large distances have either flat, polynomial or exponential decay of correlations. In this talk we will discuss work on an asymptotic expansion of the dimer-dimer correlations in a transition region. The asymptotic expansion is uniformly valid in the region between the rough and smooth phases of the two-periodic Aztec diamond and is obtained via Kasteleyn's approach. The results also apply to a related infinite graph model. We will see that there are two separate length scales involved and give an interpretation of the results. If we have time, we will also discuss some other work related to the transition region.