Logarithmic variance for the height function of square-ice
Probability
2022-02-01 v2 Mathematical Physics
math.MP
Abstract
In this article, we prove that the height function associated with the square-ice model (i.e.~the six-vertex model with on the square lattice), or, equivalently, of the uniform random homomorphisms from to , has logarithmic variance. This establishes a strong form of roughness of this height function.
Cite
@article{arxiv.1911.00092,
title = {Logarithmic variance for the height function of square-ice},
author = {Hugo Duminil-Copin and Matan Harel and Benoit Laslier and Aran Raoufi and Gourab Ray},
journal= {arXiv preprint arXiv:1911.00092},
year = {2022}
}
Comments
36 pages. Substantial revision of the RSW theorem