# Depinning in the integer-valued Gaussian Field and the BKT phase of the 2D Villain model

@inproceedings{Aizenman2021DepinningIT, title={Depinning in the integer-valued Gaussian Field and the BKT phase of the 2D Villain model}, author={Michael Aizenman and Matan Harel and Ron Peled and Jacob Shapiro}, year={2021} }

It is shown that the Villain model of two-component spins over two dimensional lattices exhibits slow, non-summable, decay of correlations at any temperature at which the dual integer-valued Gaussian field exhibits depinning. For the latter, we extend the recent proof by P. Lammers of the existence of a depinning transition in the integervalued Gaussian field in two-dimensional graphs of degree three to all doubly-periodic graphs, in particular to Z. Taken together these two statements yield a…

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