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arXiv · 1911.00092

Logarithmic variance for the height function of square-ice

Hugo Duminil-Copin·Matan Harel·Benoit Laslier·Aran Raoufi·Gourab Ray
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Abstract

In this article, we prove that the height function associated with the square-ice model (i.e.~the six-vertex model with $a=b=c=1$ on the square lattice), or, equivalently, of the uniform random homomorphisms from $\mathbb Z^2$ to $\mathbb Z$, has logarithmic variance. This establishes a strong form of roughness of this height function.

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Hugo Duminil-Copin, Matan Harel, Benoit Laslier, Aran Raoufi, Gourab Ray. 2019-10-31. Logarithmic variance for the height function of square-ice. https://arxiv.org/abs/1911.00092

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