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arXiv · 2204.06378

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

Emily Bain
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Abstract

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.

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Emily Bain. 2022-04-13. Local correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit. https://doi.org/10.1063/5.0097256

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