Emily Bain | Searcharxiv

arXiv2023

A numerical study of two-point correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit

In Bain [J. Math. Phys. 64, 023301 (2023)], we found asymptotics of one-point correlation functions of the two-periodic weighted Aztec diamond in the mesoscopic limit, where the linear size of the ordered region is of the same order as the correlation length. In this paper, we follow up with a numerical study of two-point correlation functions of dimers separated by a mesoscopic distance.

math-ph↗

arXiv2022

Local correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit

Here we study the two-periodic weighted dimer model on the Aztec diamond graph. In the thermodynamic limit when the size of the graph goes to infinity while weights are fixed, the model develops a limit shape with frozen regions near corners, a flat ``diamond'' in the center with a noncritical (ordered) phase, and a disordered phase separating this diamond and the frozen phase. We show that in the mesoscopic scaling limit, when weights scale in the thermodynamic limit such that the size of the ``flat diamond'' is of the same order as the correlation length inside the diamond, fluctuations of the height function are described by a new process. We compute asymptotics of the inverse Kasteleyn matrix for vertices in a local neighborhood in this mesoscopic limit.

math-ph↗