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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Local correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit
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February 2023
Research Article|
February 02 2023
Local correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit
Emily Bain
Emily Bain
a)
(Data curation, Formal analysis, Investigation, Software, Visualization, Writing – original draft)
University of California, Berkeley and Yau Mathematical Sciences Center, Tsinghua University
, , Berkeley, California 94720, USA and Yau Mathematical Sciences Center, Tsinghua University, Beijing, Beijing 100084, China
a)Author to whom correspondence should be addressed: emily_bain@berkeley.edu. URL: https://math.berkeley.edu/∼ebain/.
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a)Author to whom correspondence should be addressed: emily_bain@berkeley.edu. URL: https://math.berkeley.edu/∼ebain/.
J. Math. Phys. 64, 023301 (2023)
Article history
Received:
April 27 2022
Accepted:
January 11 2023
Citation
Emily Bain; Local correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit. J. Math. Phys. 1 February 2023; 64 (2): 023301. https://doi.org/10.1063/5.0097256
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