Abstract
AbstractUsing 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.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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