The Fr\"ohlich-Spencer Proof of the Berezinskii-Kosterlitz-Thouless Transition
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We present the Fr\"ohlich-Spencer proof of the Berezinskii-Kosterlitz-Thouless transition. Our treatment includes the proof of delocalization for the integer-valued discrete Gaussian free field at high temperature and the proof of existence of a phase with power-law decay of correlations in the plane rotator model with Villain interaction, both in two dimensions. The treatment differs from the original in various technical points and we hope it will be of benefit to the community.
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Cited by 2 Pith papers
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The impact of disorder and non-convex interactions on delocalisation of height functions
Phase transitions in XY/Villain models and dual height functions persist under quenched disorder, and rough phases exist for annealed non-convex potentials like |∇h|^p with p≤2.
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A dichotomy theory for the height functions of the BKT transition
The paper establishes a dichotomy for height functions at the BKT transition: localization yields exponential covariance decay while delocalization forces at least logarithmic variance growth with a universal positive...
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