The Fröhlich-Spencer Proof of the Berezinskii-Kosterlitz-Thouless Transition

Abstract

We present the Fröhlich-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.

40 pages

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