Classical theorems of Fröhlich and Spencer: the Kosterlitz–Thouless transition, massless phases of abelian gauge theories, and Anderson localization
A Lean 4 / Mathlib formalization of three papers of J. Fröhlich and T. Spencer (Communications in Mathematical Physics, 1981, 1982 and 1983), with the two-dimensional multiscale analysis in the finite-volume form of V. Kharash and R. Peled (2017). For the two-dimensional plane rotator it proves the Kosterlitz–Thouless transition: the two-point function decays exponentially at high temperature, while at low temperature it obeys the power-law lower bound of Theorem C and still tends to zero, so that there is no long-range order. The same multiscale expansion in charge ensembles gives the…
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