Depinning in the integervalued Gaussian Field and the BKT phase of the 2D Villain model
Abstract
It is shown that the Villain model of twocomponent spins over two dimensional lattices exhibits slow, nonsummable, decay of correlations at any temperature at which the dual integervalued Gaussian field exhibits depinning. For the latter, we extend the recent proof by P. Lammers of the existence of a depinning transition in the integer valued Gaussian field in two dimensional graphs of degree three to all doubly periodic graphs, in particular to $\mathbb{Z}^2$. Taken together these two statements yield a new perspective on the BerezinskiiKosterlitzThouless phase transition in the Villain model, and complete a new proof of depinning in two dimensional integervalued height functions.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09498
 Bibcode:
 2021arXiv211009498A
 Keywords:

 Mathematics  Probability;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 60D05;
 82B26
 EPrint:
 (with a more transparent presentation of the exploration process)