van Engelenburg, D., & Lis, M. (2022). An Elementary Proof of Phase Transition in the Planar XY Model. Communications in Mathematical Physics, 399(1), 85–104. https://doi.org/10.1007/s00220-022-04550-3
E105-07 - Forschungsbereich Mathematische Stochastik E105 - Institut für Stochastik und Wirtschaftsmathematik
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Journal:
Communications in Mathematical Physics
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ISSN:
0010-3616
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Date (published):
15-Nov-2022
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Number of Pages:
20
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Publisher:
SPRINGER
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Peer reviewed:
Yes
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Keywords:
Berezinskii-Kosterlitz-Thouless phase transition; XY model
en
Abstract:
Using elementary methods we obtain a power-law lower bound on the two-point function of the planar XY spin model at low temperatures. This was famously first rigorously obtained by Fröhlich and Spencer (Commun Math Phys 81(4):527–602, 1981) and establishes a Berezinskii–Kosterlitz–Thouless phase transition in the model. Our argument relies on a new loop representation of spin correlations, a recent result of Lammers (Probab Relat Fields, 2021) on delocalisation of general integer-valued height functions, and classical correlation inequalities.
CC BY 4.0
