Dimer–Dimer Correlations at the Rough–Smooth Boundary

Abstract Three phases of macroscopic domains have been seen for large but finite periodic dimer models; these are known as the frozen, rough and smooth phases. The transition region between frozen has received a lot attention last twenty years recently work underway to understand rough–smooth in case two-periodic Aztec diamond. We compute uniform asymptotics dimer–dimer correlations diamond when dimers lie region. These rely on formula found Chhita Johansson (Adv Math 294:37–149, 2016) inverse Kasteleyn matrix, they also apply infinite square grid model with variable weighting which interpolates phase (Kenyon et al. Ann (2) 163(3):1019–1056, 2006). In particular, we find that distant initially decay exponentially magnetic coordinates very close bounded complementary component associated amoebae, then power law once far enough apart.